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Simplifying 100 = -16x2 + 95x + 6 Reorder the terms: 100 = 6 + 95x + -16x2 Solving 100 = 6 + 95x + -16x2 Solving for variable 'x'. Combine like terms: 100 + -6 = 94 94 + -95x + 16x2 = 6 + 95x + -16x2 + -6 + -95x + 16x2 Reorder the terms: 94 + -95x + 16x2 = 6 + -6 + 95x + -95x + -16x2 + 16x2 Combine like terms: 6 + -6 = 0 94 + -95x + 16x2 = 0 + 95x + -95x + -16x2 + 16x2 94 + -95x + 16x2 = 95x + -95x + -16x2 + 16x2 Combine like terms: 95x + -95x = 0 94 + -95x + 16x2 = 0 + -16x2 + 16x2 94 + -95x + 16x2 = -16x2 + 16x2 Combine like terms: -16x2 + 16x2 = 0 94 + -95x + 16x2 = 0 Begin completing the square. Divide all terms by 16 the coefficient of the squared term: Divide each side by '16'. 5.875 + -5.9375x + x2 = 0 Move the constant term to the right: Add '-5.875' to each side of the equation. 5.875 + -5.9375x + -5.875 + x2 = 0 + -5.875 Reorder the terms: 5.875 + -5.875 + -5.9375x + x2 = 0 + -5.875 Combine like terms: 5.875 + -5.875 = 0.000 0.000 + -5.9375x + x2 = 0 + -5.875 -5.9375x + x2 = 0 + -5.875 Combine like terms: 0 + -5.875 = -5.875 -5.9375x + x2 = -5.875 The x term is -5.9375x. Take half its coefficient (-2.96875). Square it (8.813476563) and add it to both sides. Add '8.813476563' to each side of the equation. -5.9375x + 8.813476563 + x2 = -5.875 + 8.813476563 Reorder the terms: 8.813476563 + -5.9375x + x2 = -5.875 + 8.813476563 Combine like terms: -5.875 + 8.813476563 = 2.938476563 8.813476563 + -5.9375x + x2 = 2.938476563 Factor a perfect square on the left side: (x + -2.96875)(x + -2.96875) = 2.938476563 Calculate the square root of the right side: 1.714198519 Break this problem into two subproblems by setting (x + -2.96875) equal to 1.714198519 and -1.714198519.Subproblem 1
x + -2.96875 = 1.714198519 Simplifying x + -2.96875 = 1.714198519 Reorder the terms: -2.96875 + x = 1.714198519 Solving -2.96875 + x = 1.714198519 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.96875' to each side of the equation. -2.96875 + 2.96875 + x = 1.714198519 + 2.96875 Combine like terms: -2.96875 + 2.96875 = 0.00000 0.00000 + x = 1.714198519 + 2.96875 x = 1.714198519 + 2.96875 Combine like terms: 1.714198519 + 2.96875 = 4.682948519 x = 4.682948519 Simplifying x = 4.682948519Subproblem 2
x + -2.96875 = -1.714198519 Simplifying x + -2.96875 = -1.714198519 Reorder the terms: -2.96875 + x = -1.714198519 Solving -2.96875 + x = -1.714198519 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.96875' to each side of the equation. -2.96875 + 2.96875 + x = -1.714198519 + 2.96875 Combine like terms: -2.96875 + 2.96875 = 0.00000 0.00000 + x = -1.714198519 + 2.96875 x = -1.714198519 + 2.96875 Combine like terms: -1.714198519 + 2.96875 = 1.254551481 x = 1.254551481 Simplifying x = 1.254551481Solution
The solution to the problem is based on the solutions from the subproblems. x = {4.682948519, 1.254551481}
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