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Simplifying x2 + (20 + -3x)(20 + -3x) + -14(20 + -3x) = 0 Multiply (20 + -3x) * (20 + -3x) x2 + (20(20 + -3x) + -3x * (20 + -3x)) + -14(20 + -3x) = 0 x2 + ((20 * 20 + -3x * 20) + -3x * (20 + -3x)) + -14(20 + -3x) = 0 x2 + ((400 + -60x) + -3x * (20 + -3x)) + -14(20 + -3x) = 0 x2 + (400 + -60x + (20 * -3x + -3x * -3x)) + -14(20 + -3x) = 0 x2 + (400 + -60x + (-60x + 9x2)) + -14(20 + -3x) = 0 Combine like terms: -60x + -60x = -120x x2 + (400 + -120x + 9x2) + -14(20 + -3x) = 0 x2 + 400 + -120x + 9x2 + (20 * -14 + -3x * -14) = 0 x2 + 400 + -120x + 9x2 + (-280 + 42x) = 0 Reorder the terms: 400 + -280 + -120x + 42x + x2 + 9x2 = 0 Combine like terms: 400 + -280 = 120 120 + -120x + 42x + x2 + 9x2 = 0 Combine like terms: -120x + 42x = -78x 120 + -78x + x2 + 9x2 = 0 Combine like terms: x2 + 9x2 = 10x2 120 + -78x + 10x2 = 0 Solving 120 + -78x + 10x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '2'. 2(60 + -39x + 5x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(60 + -39x + 5x2)' equal to zero and attempt to solve: Simplifying 60 + -39x + 5x2 = 0 Solving 60 + -39x + 5x2 = 0 Begin completing the square. Divide all terms by 5 the coefficient of the squared term: Divide each side by '5'. 12 + -7.8x + x2 = 0 Move the constant term to the right: Add '-12' to each side of the equation. 12 + -7.8x + -12 + x2 = 0 + -12 Reorder the terms: 12 + -12 + -7.8x + x2 = 0 + -12 Combine like terms: 12 + -12 = 0 0 + -7.8x + x2 = 0 + -12 -7.8x + x2 = 0 + -12 Combine like terms: 0 + -12 = -12 -7.8x + x2 = -12 The x term is -7.8x. Take half its coefficient (-3.9). Square it (15.21) and add it to both sides. Add '15.21' to each side of the equation. -7.8x + 15.21 + x2 = -12 + 15.21 Reorder the terms: 15.21 + -7.8x + x2 = -12 + 15.21 Combine like terms: -12 + 15.21 = 3.21 15.21 + -7.8x + x2 = 3.21 Factor a perfect square on the left side: (x + -3.9)(x + -3.9) = 3.21 Calculate the square root of the right side: 1.791647287 Break this problem into two subproblems by setting (x + -3.9) equal to 1.791647287 and -1.791647287.Subproblem 1
x + -3.9 = 1.791647287 Simplifying x + -3.9 = 1.791647287 Reorder the terms: -3.9 + x = 1.791647287 Solving -3.9 + x = 1.791647287 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '3.9' to each side of the equation. -3.9 + 3.9 + x = 1.791647287 + 3.9 Combine like terms: -3.9 + 3.9 = 0.0 0.0 + x = 1.791647287 + 3.9 x = 1.791647287 + 3.9 Combine like terms: 1.791647287 + 3.9 = 5.691647287 x = 5.691647287 Simplifying x = 5.691647287Subproblem 2
x + -3.9 = -1.791647287 Simplifying x + -3.9 = -1.791647287 Reorder the terms: -3.9 + x = -1.791647287 Solving -3.9 + x = -1.791647287 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '3.9' to each side of the equation. -3.9 + 3.9 + x = -1.791647287 + 3.9 Combine like terms: -3.9 + 3.9 = 0.0 0.0 + x = -1.791647287 + 3.9 x = -1.791647287 + 3.9 Combine like terms: -1.791647287 + 3.9 = 2.108352713 x = 2.108352713 Simplifying x = 2.108352713Solution
The solution to the problem is based on the solutions from the subproblems. x = {5.691647287, 2.108352713}Solution
x = {5.691647287, 2.108352713}
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