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Simplifying 0 = -0.64x2 + 24x + 3 Reorder the terms: 0 = 3 + 24x + -0.64x2 Solving 0 = 3 + 24x + -0.64x2 Solving for variable 'x'. Combine like terms: 0 + -3 = -3 -3 + -24x + 0.64x2 = 3 + 24x + -0.64x2 + -3 + -24x + 0.64x2 Reorder the terms: -3 + -24x + 0.64x2 = 3 + -3 + 24x + -24x + -0.64x2 + 0.64x2 Combine like terms: 3 + -3 = 0 -3 + -24x + 0.64x2 = 0 + 24x + -24x + -0.64x2 + 0.64x2 -3 + -24x + 0.64x2 = 24x + -24x + -0.64x2 + 0.64x2 Combine like terms: 24x + -24x = 0 -3 + -24x + 0.64x2 = 0 + -0.64x2 + 0.64x2 -3 + -24x + 0.64x2 = -0.64x2 + 0.64x2 Combine like terms: -0.64x2 + 0.64x2 = 0.00 -3 + -24x + 0.64x2 = 0.00 Begin completing the square. Divide all terms by 0.64 the coefficient of the squared term: Divide each side by '0.64'. -4.6875 + -37.5x + x2 = 0 Move the constant term to the right: Add '4.6875' to each side of the equation. -4.6875 + -37.5x + 4.6875 + x2 = 0 + 4.6875 Reorder the terms: -4.6875 + 4.6875 + -37.5x + x2 = 0 + 4.6875 Combine like terms: -4.6875 + 4.6875 = 0.0000 0.0000 + -37.5x + x2 = 0 + 4.6875 -37.5x + x2 = 0 + 4.6875 Combine like terms: 0 + 4.6875 = 4.6875 -37.5x + x2 = 4.6875 The x term is -37.5x. Take half its coefficient (-18.75). Square it (351.5625) and add it to both sides. Add '351.5625' to each side of the equation. -37.5x + 351.5625 + x2 = 4.6875 + 351.5625 Reorder the terms: 351.5625 + -37.5x + x2 = 4.6875 + 351.5625 Combine like terms: 4.6875 + 351.5625 = 356.25 351.5625 + -37.5x + x2 = 356.25 Factor a perfect square on the left side: (x + -18.75)(x + -18.75) = 356.25 Calculate the square root of the right side: 18.874586088 Break this problem into two subproblems by setting (x + -18.75) equal to 18.874586088 and -18.874586088.Subproblem 1
x + -18.75 = 18.874586088 Simplifying x + -18.75 = 18.874586088 Reorder the terms: -18.75 + x = 18.874586088 Solving -18.75 + x = 18.874586088 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '18.75' to each side of the equation. -18.75 + 18.75 + x = 18.874586088 + 18.75 Combine like terms: -18.75 + 18.75 = 0.00 0.00 + x = 18.874586088 + 18.75 x = 18.874586088 + 18.75 Combine like terms: 18.874586088 + 18.75 = 37.624586088 x = 37.624586088 Simplifying x = 37.624586088Subproblem 2
x + -18.75 = -18.874586088 Simplifying x + -18.75 = -18.874586088 Reorder the terms: -18.75 + x = -18.874586088 Solving -18.75 + x = -18.874586088 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '18.75' to each side of the equation. -18.75 + 18.75 + x = -18.874586088 + 18.75 Combine like terms: -18.75 + 18.75 = 0.00 0.00 + x = -18.874586088 + 18.75 x = -18.874586088 + 18.75 Combine like terms: -18.874586088 + 18.75 = -0.124586088 x = -0.124586088 Simplifying x = -0.124586088Solution
The solution to the problem is based on the solutions from the subproblems. x = {37.624586088, -0.124586088}
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