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Simplifying -0.04x2 + 0.64x + 1.94 = 0 Reorder the terms: 1.94 + 0.64x + -0.04x2 = 0 Solving 1.94 + 0.64x + -0.04x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by -0.04 the coefficient of the squared term: Divide each side by '-0.04'. -48.5 + -16x + x2 = 0 Move the constant term to the right: Add '48.5' to each side of the equation. -48.5 + -16x + 48.5 + x2 = 0 + 48.5 Reorder the terms: -48.5 + 48.5 + -16x + x2 = 0 + 48.5 Combine like terms: -48.5 + 48.5 = 0.0 0.0 + -16x + x2 = 0 + 48.5 -16x + x2 = 0 + 48.5 Combine like terms: 0 + 48.5 = 48.5 -16x + x2 = 48.5 The x term is -16x. Take half its coefficient (-8). Square it (64) and add it to both sides. Add '64' to each side of the equation. -16x + 64 + x2 = 48.5 + 64 Reorder the terms: 64 + -16x + x2 = 48.5 + 64 Combine like terms: 48.5 + 64 = 112.5 64 + -16x + x2 = 112.5 Factor a perfect square on the left side: (x + -8)(x + -8) = 112.5 Calculate the square root of the right side: 10.606601718 Break this problem into two subproblems by setting (x + -8) equal to 10.606601718 and -10.606601718.Subproblem 1
x + -8 = 10.606601718 Simplifying x + -8 = 10.606601718 Reorder the terms: -8 + x = 10.606601718 Solving -8 + x = 10.606601718 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '8' to each side of the equation. -8 + 8 + x = 10.606601718 + 8 Combine like terms: -8 + 8 = 0 0 + x = 10.606601718 + 8 x = 10.606601718 + 8 Combine like terms: 10.606601718 + 8 = 18.606601718 x = 18.606601718 Simplifying x = 18.606601718Subproblem 2
x + -8 = -10.606601718 Simplifying x + -8 = -10.606601718 Reorder the terms: -8 + x = -10.606601718 Solving -8 + x = -10.606601718 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '8' to each side of the equation. -8 + 8 + x = -10.606601718 + 8 Combine like terms: -8 + 8 = 0 0 + x = -10.606601718 + 8 x = -10.606601718 + 8 Combine like terms: -10.606601718 + 8 = -2.606601718 x = -2.606601718 Simplifying x = -2.606601718Solution
The solution to the problem is based on the solutions from the subproblems. x = {18.606601718, -2.606601718}
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