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Simplifying 9x2 + -5x = 157 Reorder the terms: -5x + 9x2 = 157 Solving -5x + 9x2 = 157 Solving for variable 'x'. Reorder the terms: -157 + -5x + 9x2 = 157 + -157 Combine like terms: 157 + -157 = 0 -157 + -5x + 9x2 = 0 Begin completing the square. Divide all terms by 9 the coefficient of the squared term: Divide each side by '9'. -17.44444444 + -0.5555555556x + x2 = 0 Move the constant term to the right: Add '17.44444444' to each side of the equation. -17.44444444 + -0.5555555556x + 17.44444444 + x2 = 0 + 17.44444444 Reorder the terms: -17.44444444 + 17.44444444 + -0.5555555556x + x2 = 0 + 17.44444444 Combine like terms: -17.44444444 + 17.44444444 = 0.00000000 0.00000000 + -0.5555555556x + x2 = 0 + 17.44444444 -0.5555555556x + x2 = 0 + 17.44444444 Combine like terms: 0 + 17.44444444 = 17.44444444 -0.5555555556x + x2 = 17.44444444 The x term is -0.5555555556x. Take half its coefficient (-0.2777777778). Square it (0.07716049384) and add it to both sides. Add '0.07716049384' to each side of the equation. -0.5555555556x + 0.07716049384 + x2 = 17.44444444 + 0.07716049384 Reorder the terms: 0.07716049384 + -0.5555555556x + x2 = 17.44444444 + 0.07716049384 Combine like terms: 17.44444444 + 0.07716049384 = 17.52160493384 0.07716049384 + -0.5555555556x + x2 = 17.52160493384 Factor a perfect square on the left side: (x + -0.2777777778)(x + -0.2777777778) = 17.52160493384 Calculate the square root of the right side: 4.18588162 Break this problem into two subproblems by setting (x + -0.2777777778) equal to 4.18588162 and -4.18588162.Subproblem 1
x + -0.2777777778 = 4.18588162 Simplifying x + -0.2777777778 = 4.18588162 Reorder the terms: -0.2777777778 + x = 4.18588162 Solving -0.2777777778 + x = 4.18588162 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.2777777778' to each side of the equation. -0.2777777778 + 0.2777777778 + x = 4.18588162 + 0.2777777778 Combine like terms: -0.2777777778 + 0.2777777778 = 0.0000000000 0.0000000000 + x = 4.18588162 + 0.2777777778 x = 4.18588162 + 0.2777777778 Combine like terms: 4.18588162 + 0.2777777778 = 4.4636593978 x = 4.4636593978 Simplifying x = 4.4636593978Subproblem 2
x + -0.2777777778 = -4.18588162 Simplifying x + -0.2777777778 = -4.18588162 Reorder the terms: -0.2777777778 + x = -4.18588162 Solving -0.2777777778 + x = -4.18588162 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.2777777778' to each side of the equation. -0.2777777778 + 0.2777777778 + x = -4.18588162 + 0.2777777778 Combine like terms: -0.2777777778 + 0.2777777778 = 0.0000000000 0.0000000000 + x = -4.18588162 + 0.2777777778 x = -4.18588162 + 0.2777777778 Combine like terms: -4.18588162 + 0.2777777778 = -3.9081038422 x = -3.9081038422 Simplifying x = -3.9081038422Solution
The solution to the problem is based on the solutions from the subproblems. x = {4.4636593978, -3.9081038422}
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