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Simplifying 2x2 + -21x = -25 Reorder the terms: -21x + 2x2 = -25 Solving -21x + 2x2 = -25 Solving for variable 'x'. Reorder the terms: 25 + -21x + 2x2 = -25 + 25 Combine like terms: -25 + 25 = 0 25 + -21x + 2x2 = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. 12.5 + -10.5x + x2 = 0 Move the constant term to the right: Add '-12.5' to each side of the equation. 12.5 + -10.5x + -12.5 + x2 = 0 + -12.5 Reorder the terms: 12.5 + -12.5 + -10.5x + x2 = 0 + -12.5 Combine like terms: 12.5 + -12.5 = 0.0 0.0 + -10.5x + x2 = 0 + -12.5 -10.5x + x2 = 0 + -12.5 Combine like terms: 0 + -12.5 = -12.5 -10.5x + x2 = -12.5 The x term is -10.5x. Take half its coefficient (-5.25). Square it (27.5625) and add it to both sides. Add '27.5625' to each side of the equation. -10.5x + 27.5625 + x2 = -12.5 + 27.5625 Reorder the terms: 27.5625 + -10.5x + x2 = -12.5 + 27.5625 Combine like terms: -12.5 + 27.5625 = 15.0625 27.5625 + -10.5x + x2 = 15.0625 Factor a perfect square on the left side: (x + -5.25)(x + -5.25) = 15.0625 Calculate the square root of the right side: 3.881043674 Break this problem into two subproblems by setting (x + -5.25) equal to 3.881043674 and -3.881043674.Subproblem 1
x + -5.25 = 3.881043674 Simplifying x + -5.25 = 3.881043674 Reorder the terms: -5.25 + x = 3.881043674 Solving -5.25 + x = 3.881043674 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '5.25' to each side of the equation. -5.25 + 5.25 + x = 3.881043674 + 5.25 Combine like terms: -5.25 + 5.25 = 0.00 0.00 + x = 3.881043674 + 5.25 x = 3.881043674 + 5.25 Combine like terms: 3.881043674 + 5.25 = 9.131043674 x = 9.131043674 Simplifying x = 9.131043674Subproblem 2
x + -5.25 = -3.881043674 Simplifying x + -5.25 = -3.881043674 Reorder the terms: -5.25 + x = -3.881043674 Solving -5.25 + x = -3.881043674 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '5.25' to each side of the equation. -5.25 + 5.25 + x = -3.881043674 + 5.25 Combine like terms: -5.25 + 5.25 = 0.00 0.00 + x = -3.881043674 + 5.25 x = -3.881043674 + 5.25 Combine like terms: -3.881043674 + 5.25 = 1.368956326 x = 1.368956326 Simplifying x = 1.368956326Solution
The solution to the problem is based on the solutions from the subproblems. x = {9.131043674, 1.368956326}
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