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Simplifying x2 + (-0.429x + 15)(-0.429x + 15) + -12x + -16(-0.429x + 15) + 71 = 0 Reorder the terms: x2 + (15 + -0.429x)(-0.429x + 15) + -12x + -16(-0.429x + 15) + 71 = 0 Reorder the terms: x2 + (15 + -0.429x)(15 + -0.429x) + -12x + -16(-0.429x + 15) + 71 = 0 Multiply (15 + -0.429x) * (15 + -0.429x) x2 + (15(15 + -0.429x) + -0.429x * (15 + -0.429x)) + -12x + -16(-0.429x + 15) + 71 = 0 x2 + ((15 * 15 + -0.429x * 15) + -0.429x * (15 + -0.429x)) + -12x + -16(-0.429x + 15) + 71 = 0 x2 + ((225 + -6.435x) + -0.429x * (15 + -0.429x)) + -12x + -16(-0.429x + 15) + 71 = 0 x2 + (225 + -6.435x + (15 * -0.429x + -0.429x * -0.429x)) + -12x + -16(-0.429x + 15) + 71 = 0 x2 + (225 + -6.435x + (-6.435x + 0.184041x2)) + -12x + -16(-0.429x + 15) + 71 = 0 Combine like terms: -6.435x + -6.435x = -12.87x x2 + (225 + -12.87x + 0.184041x2) + -12x + -16(-0.429x + 15) + 71 = 0 Reorder the terms: x2 + 225 + -12.87x + 0.184041x2 + -12x + -16(15 + -0.429x) + 71 = 0 x2 + 225 + -12.87x + 0.184041x2 + -12x + (15 * -16 + -0.429x * -16) + 71 = 0 x2 + 225 + -12.87x + 0.184041x2 + -12x + (-240 + 6.864x) + 71 = 0 Reorder the terms: 225 + -240 + 71 + -12.87x + -12x + 6.864x + x2 + 0.184041x2 = 0 Combine like terms: 225 + -240 = -15 -15 + 71 + -12.87x + -12x + 6.864x + x2 + 0.184041x2 = 0 Combine like terms: -15 + 71 = 56 56 + -12.87x + -12x + 6.864x + x2 + 0.184041x2 = 0 Combine like terms: -12.87x + -12x = -24.87x 56 + -24.87x + 6.864x + x2 + 0.184041x2 = 0 Combine like terms: -24.87x + 6.864x = -18.006x 56 + -18.006x + x2 + 0.184041x2 = 0 Combine like terms: x2 + 0.184041x2 = 1.184041x2 56 + -18.006x + 1.184041x2 = 0 Solving 56 + -18.006x + 1.184041x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 1.184041 the coefficient of the squared term: Divide each side by '1.184041'. 47.29565953 + -15.20724367x + x2 = 0 Move the constant term to the right: Add '-47.29565953' to each side of the equation. 47.29565953 + -15.20724367x + -47.29565953 + x2 = 0 + -47.29565953 Reorder the terms: 47.29565953 + -47.29565953 + -15.20724367x + x2 = 0 + -47.29565953 Combine like terms: 47.29565953 + -47.29565953 = 0.00000000 0.00000000 + -15.20724367x + x2 = 0 + -47.29565953 -15.20724367x + x2 = 0 + -47.29565953 Combine like terms: 0 + -47.29565953 = -47.29565953 -15.20724367x + x2 = -47.29565953 The x term is -15.20724367x. Take half its coefficient (-7.603621835). Square it (57.81506501) and add it to both sides. Add '57.81506501' to each side of the equation. -15.20724367x + 57.81506501 + x2 = -47.29565953 + 57.81506501 Reorder the terms: 57.81506501 + -15.20724367x + x2 = -47.29565953 + 57.81506501 Combine like terms: -47.29565953 + 57.81506501 = 10.51940548 57.81506501 + -15.20724367x + x2 = 10.51940548 Factor a perfect square on the left side: (x + -7.603621835)(x + -7.603621835) = 10.51940548 Calculate the square root of the right side: 3.243363298 Break this problem into two subproblems by setting (x + -7.603621835) equal to 3.243363298 and -3.243363298.Subproblem 1
x + -7.603621835 = 3.243363298 Simplifying x + -7.603621835 = 3.243363298 Reorder the terms: -7.603621835 + x = 3.243363298 Solving -7.603621835 + x = 3.243363298 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '7.603621835' to each side of the equation. -7.603621835 + 7.603621835 + x = 3.243363298 + 7.603621835 Combine like terms: -7.603621835 + 7.603621835 = 0.000000000 0.000000000 + x = 3.243363298 + 7.603621835 x = 3.243363298 + 7.603621835 Combine like terms: 3.243363298 + 7.603621835 = 10.846985133 x = 10.846985133 Simplifying x = 10.846985133Subproblem 2
x + -7.603621835 = -3.243363298 Simplifying x + -7.603621835 = -3.243363298 Reorder the terms: -7.603621835 + x = -3.243363298 Solving -7.603621835 + x = -3.243363298 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '7.603621835' to each side of the equation. -7.603621835 + 7.603621835 + x = -3.243363298 + 7.603621835 Combine like terms: -7.603621835 + 7.603621835 = 0.000000000 0.000000000 + x = -3.243363298 + 7.603621835 x = -3.243363298 + 7.603621835 Combine like terms: -3.243363298 + 7.603621835 = 4.360258537 x = 4.360258537 Simplifying x = 4.360258537Solution
The solution to the problem is based on the solutions from the subproblems. x = {10.846985133, 4.360258537}
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