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Simplifying 4x2 + -66x + 105 = 0 Reorder the terms: 105 + -66x + 4x2 = 0 Solving 105 + -66x + 4x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 4 the coefficient of the squared term: Divide each side by '4'. 26.25 + -16.5x + x2 = 0 Move the constant term to the right: Add '-26.25' to each side of the equation. 26.25 + -16.5x + -26.25 + x2 = 0 + -26.25 Reorder the terms: 26.25 + -26.25 + -16.5x + x2 = 0 + -26.25 Combine like terms: 26.25 + -26.25 = 0.00 0.00 + -16.5x + x2 = 0 + -26.25 -16.5x + x2 = 0 + -26.25 Combine like terms: 0 + -26.25 = -26.25 -16.5x + x2 = -26.25 The x term is -16.5x. Take half its coefficient (-8.25). Square it (68.0625) and add it to both sides. Add '68.0625' to each side of the equation. -16.5x + 68.0625 + x2 = -26.25 + 68.0625 Reorder the terms: 68.0625 + -16.5x + x2 = -26.25 + 68.0625 Combine like terms: -26.25 + 68.0625 = 41.8125 68.0625 + -16.5x + x2 = 41.8125 Factor a perfect square on the left side: (x + -8.25)(x + -8.25) = 41.8125 Calculate the square root of the right side: 6.466258578 Break this problem into two subproblems by setting (x + -8.25) equal to 6.466258578 and -6.466258578.Subproblem 1
x + -8.25 = 6.466258578 Simplifying x + -8.25 = 6.466258578 Reorder the terms: -8.25 + x = 6.466258578 Solving -8.25 + x = 6.466258578 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '8.25' to each side of the equation. -8.25 + 8.25 + x = 6.466258578 + 8.25 Combine like terms: -8.25 + 8.25 = 0.00 0.00 + x = 6.466258578 + 8.25 x = 6.466258578 + 8.25 Combine like terms: 6.466258578 + 8.25 = 14.716258578 x = 14.716258578 Simplifying x = 14.716258578Subproblem 2
x + -8.25 = -6.466258578 Simplifying x + -8.25 = -6.466258578 Reorder the terms: -8.25 + x = -6.466258578 Solving -8.25 + x = -6.466258578 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '8.25' to each side of the equation. -8.25 + 8.25 + x = -6.466258578 + 8.25 Combine like terms: -8.25 + 8.25 = 0.00 0.00 + x = -6.466258578 + 8.25 x = -6.466258578 + 8.25 Combine like terms: -6.466258578 + 8.25 = 1.783741422 x = 1.783741422 Simplifying x = 1.783741422Solution
The solution to the problem is based on the solutions from the subproblems. x = {14.716258578, 1.783741422}
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