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Simplifying -16x2 + 69x + 288 = 0 Reorder the terms: 288 + 69x + -16x2 = 0 Solving 288 + 69x + -16x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by -16 the coefficient of the squared term: Divide each side by '-16'. -18 + -4.3125x + x2 = 0 Move the constant term to the right: Add '18' to each side of the equation. -18 + -4.3125x + 18 + x2 = 0 + 18 Reorder the terms: -18 + 18 + -4.3125x + x2 = 0 + 18 Combine like terms: -18 + 18 = 0 0 + -4.3125x + x2 = 0 + 18 -4.3125x + x2 = 0 + 18 Combine like terms: 0 + 18 = 18 -4.3125x + x2 = 18 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 = 18 + 4.649414063 Reorder the terms: 4.649414063 + -4.3125x + x2 = 18 + 4.649414063 Combine like terms: 18 + 4.649414063 = 22.649414063 4.649414063 + -4.3125x + x2 = 22.649414063 Factor a perfect square on the left side: (x + -2.15625)(x + -2.15625) = 22.649414063 Calculate the square root of the right side: 4.759140055 Break this problem into two subproblems by setting (x + -2.15625) equal to 4.759140055 and -4.759140055.Subproblem 1
x + -2.15625 = 4.759140055 Simplifying x + -2.15625 = 4.759140055 Reorder the terms: -2.15625 + x = 4.759140055 Solving -2.15625 + x = 4.759140055 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 = 4.759140055 + 2.15625 Combine like terms: -2.15625 + 2.15625 = 0.00000 0.00000 + x = 4.759140055 + 2.15625 x = 4.759140055 + 2.15625 Combine like terms: 4.759140055 + 2.15625 = 6.915390055 x = 6.915390055 Simplifying x = 6.915390055Subproblem 2
x + -2.15625 = -4.759140055 Simplifying x + -2.15625 = -4.759140055 Reorder the terms: -2.15625 + x = -4.759140055 Solving -2.15625 + x = -4.759140055 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 = -4.759140055 + 2.15625 Combine like terms: -2.15625 + 2.15625 = 0.00000 0.00000 + x = -4.759140055 + 2.15625 x = -4.759140055 + 2.15625 Combine like terms: -4.759140055 + 2.15625 = -2.602890055 x = -2.602890055 Simplifying x = -2.602890055Solution
The solution to the problem is based on the solutions from the subproblems. x = {6.915390055, -2.602890055}
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