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Simplifying -16x2 + 215x + 14 = 0 Reorder the terms: 14 + 215x + -16x2 = 0 Solving 14 + 215x + -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'. -0.875 + -13.4375x + x2 = 0 Move the constant term to the right: Add '0.875' to each side of the equation. -0.875 + -13.4375x + 0.875 + x2 = 0 + 0.875 Reorder the terms: -0.875 + 0.875 + -13.4375x + x2 = 0 + 0.875 Combine like terms: -0.875 + 0.875 = 0.000 0.000 + -13.4375x + x2 = 0 + 0.875 -13.4375x + x2 = 0 + 0.875 Combine like terms: 0 + 0.875 = 0.875 -13.4375x + x2 = 0.875 The x term is -13.4375x. Take half its coefficient (-6.71875). Square it (45.14160156) and add it to both sides. Add '45.14160156' to each side of the equation. -13.4375x + 45.14160156 + x2 = 0.875 + 45.14160156 Reorder the terms: 45.14160156 + -13.4375x + x2 = 0.875 + 45.14160156 Combine like terms: 0.875 + 45.14160156 = 46.01660156 45.14160156 + -13.4375x + x2 = 46.01660156 Factor a perfect square on the left side: (x + -6.71875)(x + -6.71875) = 46.01660156 Calculate the square root of the right side: 6.783553756 Break this problem into two subproblems by setting (x + -6.71875) equal to 6.783553756 and -6.783553756.Subproblem 1
x + -6.71875 = 6.783553756 Simplifying x + -6.71875 = 6.783553756 Reorder the terms: -6.71875 + x = 6.783553756 Solving -6.71875 + x = 6.783553756 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '6.71875' to each side of the equation. -6.71875 + 6.71875 + x = 6.783553756 + 6.71875 Combine like terms: -6.71875 + 6.71875 = 0.00000 0.00000 + x = 6.783553756 + 6.71875 x = 6.783553756 + 6.71875 Combine like terms: 6.783553756 + 6.71875 = 13.502303756 x = 13.502303756 Simplifying x = 13.502303756Subproblem 2
x + -6.71875 = -6.783553756 Simplifying x + -6.71875 = -6.783553756 Reorder the terms: -6.71875 + x = -6.783553756 Solving -6.71875 + x = -6.783553756 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '6.71875' to each side of the equation. -6.71875 + 6.71875 + x = -6.783553756 + 6.71875 Combine like terms: -6.71875 + 6.71875 = 0.00000 0.00000 + x = -6.783553756 + 6.71875 x = -6.783553756 + 6.71875 Combine like terms: -6.783553756 + 6.71875 = -0.064803756 x = -0.064803756 Simplifying x = -0.064803756Solution
The solution to the problem is based on the solutions from the subproblems. x = {13.502303756, -0.064803756}
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