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Simplifying 1.6x2 + -10.0x + 6.2 = 9 Reorder the terms: 6.2 + -10.0x + 1.6x2 = 9 Solving 6.2 + -10.0x + 1.6x2 = 9 Solving for variable 'x'. Reorder the terms: 6.2 + -9 + -10.0x + 1.6x2 = 9 + -9 Combine like terms: 6.2 + -9 = -2.8 -2.8 + -10.0x + 1.6x2 = 9 + -9 Combine like terms: 9 + -9 = 0 -2.8 + -10.0x + 1.6x2 = 0 Begin completing the square. Divide all terms by 1.6 the coefficient of the squared term: Divide each side by '1.6'. -1.75 + -6.25x + x2 = 0 Move the constant term to the right: Add '1.75' to each side of the equation. -1.75 + -6.25x + 1.75 + x2 = 0 + 1.75 Reorder the terms: -1.75 + 1.75 + -6.25x + x2 = 0 + 1.75 Combine like terms: -1.75 + 1.75 = 0.00 0.00 + -6.25x + x2 = 0 + 1.75 -6.25x + x2 = 0 + 1.75 Combine like terms: 0 + 1.75 = 1.75 -6.25x + x2 = 1.75 The x term is -6.25x. Take half its coefficient (-3.125). Square it (9.765625) and add it to both sides. Add '9.765625' to each side of the equation. -6.25x + 9.765625 + x2 = 1.75 + 9.765625 Reorder the terms: 9.765625 + -6.25x + x2 = 1.75 + 9.765625 Combine like terms: 1.75 + 9.765625 = 11.515625 9.765625 + -6.25x + x2 = 11.515625 Factor a perfect square on the left side: (x + -3.125)(x + -3.125) = 11.515625 Calculate the square root of the right side: 3.39346799 Break this problem into two subproblems by setting (x + -3.125) equal to 3.39346799 and -3.39346799.Subproblem 1
x + -3.125 = 3.39346799 Simplifying x + -3.125 = 3.39346799 Reorder the terms: -3.125 + x = 3.39346799 Solving -3.125 + x = 3.39346799 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '3.125' to each side of the equation. -3.125 + 3.125 + x = 3.39346799 + 3.125 Combine like terms: -3.125 + 3.125 = 0.000 0.000 + x = 3.39346799 + 3.125 x = 3.39346799 + 3.125 Combine like terms: 3.39346799 + 3.125 = 6.51846799 x = 6.51846799 Simplifying x = 6.51846799Subproblem 2
x + -3.125 = -3.39346799 Simplifying x + -3.125 = -3.39346799 Reorder the terms: -3.125 + x = -3.39346799 Solving -3.125 + x = -3.39346799 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '3.125' to each side of the equation. -3.125 + 3.125 + x = -3.39346799 + 3.125 Combine like terms: -3.125 + 3.125 = 0.000 0.000 + x = -3.39346799 + 3.125 x = -3.39346799 + 3.125 Combine like terms: -3.39346799 + 3.125 = -0.26846799 x = -0.26846799 Simplifying x = -0.26846799Solution
The solution to the problem is based on the solutions from the subproblems. x = {6.51846799, -0.26846799}
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