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Simplifying x = -16x2 + 70x + 4 Reorder the terms: x = 4 + 70x + -16x2 Solving x = 4 + 70x + -16x2 Solving for variable 'x'. Reorder the terms: -4 + x + -70x + 16x2 = 4 + 70x + -16x2 + -4 + -70x + 16x2 Combine like terms: x + -70x = -69x -4 + -69x + 16x2 = 4 + 70x + -16x2 + -4 + -70x + 16x2 Reorder the terms: -4 + -69x + 16x2 = 4 + -4 + 70x + -70x + -16x2 + 16x2 Combine like terms: 4 + -4 = 0 -4 + -69x + 16x2 = 0 + 70x + -70x + -16x2 + 16x2 -4 + -69x + 16x2 = 70x + -70x + -16x2 + 16x2 Combine like terms: 70x + -70x = 0 -4 + -69x + 16x2 = 0 + -16x2 + 16x2 -4 + -69x + 16x2 = -16x2 + 16x2 Combine like terms: -16x2 + 16x2 = 0 -4 + -69x + 16x2 = 0 Begin completing the square. Divide all terms by 16 the coefficient of the squared term: Divide each side by '16'. -0.25 + -4.3125x + x2 = 0 Move the constant term to the right: Add '0.25' to each side of the equation. -0.25 + -4.3125x + 0.25 + x2 = 0 + 0.25 Reorder the terms: -0.25 + 0.25 + -4.3125x + x2 = 0 + 0.25 Combine like terms: -0.25 + 0.25 = 0.00 0.00 + -4.3125x + x2 = 0 + 0.25 -4.3125x + x2 = 0 + 0.25 Combine like terms: 0 + 0.25 = 0.25 -4.3125x + x2 = 0.25 The x term is -4.3125x. Take half its coefficient (-2.15625). Square it (4.649414063) and add it to both sides. Add '4.649414063' to each side of the equation. -4.3125x + 4.649414063 + x2 = 0.25 + 4.649414063 Reorder the terms: 4.649414063 + -4.3125x + x2 = 0.25 + 4.649414063 Combine like terms: 0.25 + 4.649414063 = 4.899414063 4.649414063 + -4.3125x + x2 = 4.899414063 Factor a perfect square on the left side: (x + -2.15625)(x + -2.15625) = 4.899414063 Calculate the square root of the right side: 2.213462008 Break this problem into two subproblems by setting (x + -2.15625) equal to 2.213462008 and -2.213462008.Subproblem 1
x + -2.15625 = 2.213462008 Simplifying x + -2.15625 = 2.213462008 Reorder the terms: -2.15625 + x = 2.213462008 Solving -2.15625 + x = 2.213462008 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.15625' to each side of the equation. -2.15625 + 2.15625 + x = 2.213462008 + 2.15625 Combine like terms: -2.15625 + 2.15625 = 0.00000 0.00000 + x = 2.213462008 + 2.15625 x = 2.213462008 + 2.15625 Combine like terms: 2.213462008 + 2.15625 = 4.369712008 x = 4.369712008 Simplifying x = 4.369712008Subproblem 2
x + -2.15625 = -2.213462008 Simplifying x + -2.15625 = -2.213462008 Reorder the terms: -2.15625 + x = -2.213462008 Solving -2.15625 + x = -2.213462008 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.15625' to each side of the equation. -2.15625 + 2.15625 + x = -2.213462008 + 2.15625 Combine like terms: -2.15625 + 2.15625 = 0.00000 0.00000 + x = -2.213462008 + 2.15625 x = -2.213462008 + 2.15625 Combine like terms: -2.213462008 + 2.15625 = -0.057212008 x = -0.057212008 Simplifying x = -0.057212008Solution
The solution to the problem is based on the solutions from the subproblems. x = {4.369712008, -0.057212008}
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