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Simplifying x(2x + -4) = 63 Reorder the terms: x(-4 + 2x) = 63 (-4 * x + 2x * x) = 63 (-4x + 2x2) = 63 Solving -4x + 2x2 = 63 Solving for variable 'x'. Reorder the terms: -63 + -4x + 2x2 = 63 + -63 Combine like terms: 63 + -63 = 0 -63 + -4x + 2x2 = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. -31.5 + -2x + x2 = 0 Move the constant term to the right: Add '31.5' to each side of the equation. -31.5 + -2x + 31.5 + x2 = 0 + 31.5 Reorder the terms: -31.5 + 31.5 + -2x + x2 = 0 + 31.5 Combine like terms: -31.5 + 31.5 = 0.0 0.0 + -2x + x2 = 0 + 31.5 -2x + x2 = 0 + 31.5 Combine like terms: 0 + 31.5 = 31.5 -2x + x2 = 31.5 The x term is -2x. Take half its coefficient (-1). Square it (1) and add it to both sides. Add '1' to each side of the equation. -2x + 1 + x2 = 31.5 + 1 Reorder the terms: 1 + -2x + x2 = 31.5 + 1 Combine like terms: 31.5 + 1 = 32.5 1 + -2x + x2 = 32.5 Factor a perfect square on the left side: (x + -1)(x + -1) = 32.5 Calculate the square root of the right side: 5.700877125 Break this problem into two subproblems by setting (x + -1) equal to 5.700877125 and -5.700877125.Subproblem 1
x + -1 = 5.700877125 Simplifying x + -1 = 5.700877125 Reorder the terms: -1 + x = 5.700877125 Solving -1 + x = 5.700877125 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1' to each side of the equation. -1 + 1 + x = 5.700877125 + 1 Combine like terms: -1 + 1 = 0 0 + x = 5.700877125 + 1 x = 5.700877125 + 1 Combine like terms: 5.700877125 + 1 = 6.700877125 x = 6.700877125 Simplifying x = 6.700877125Subproblem 2
x + -1 = -5.700877125 Simplifying x + -1 = -5.700877125 Reorder the terms: -1 + x = -5.700877125 Solving -1 + x = -5.700877125 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1' to each side of the equation. -1 + 1 + x = -5.700877125 + 1 Combine like terms: -1 + 1 = 0 0 + x = -5.700877125 + 1 x = -5.700877125 + 1 Combine like terms: -5.700877125 + 1 = -4.700877125 x = -4.700877125 Simplifying x = -4.700877125Solution
The solution to the problem is based on the solutions from the subproblems. x = {6.700877125, -4.700877125}
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