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Simplifying 2(x2 + -48) = x Reorder the terms: 2(-48 + x2) = x (-48 * 2 + x2 * 2) = x (-96 + 2x2) = x Solving -96 + 2x2 = x Solving for variable 'x'. Reorder the terms: -96 + -1x + 2x2 = x + -1x Combine like terms: x + -1x = 0 -96 + -1x + 2x2 = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. -48 + -0.5x + x2 = 0 Move the constant term to the right: Add '48' to each side of the equation. -48 + -0.5x + 48 + x2 = 0 + 48 Reorder the terms: -48 + 48 + -0.5x + x2 = 0 + 48 Combine like terms: -48 + 48 = 0 0 + -0.5x + x2 = 0 + 48 -0.5x + x2 = 0 + 48 Combine like terms: 0 + 48 = 48 -0.5x + x2 = 48 The x term is -0.5x. Take half its coefficient (-0.25). Square it (0.0625) and add it to both sides. Add '0.0625' to each side of the equation. -0.5x + 0.0625 + x2 = 48 + 0.0625 Reorder the terms: 0.0625 + -0.5x + x2 = 48 + 0.0625 Combine like terms: 48 + 0.0625 = 48.0625 0.0625 + -0.5x + x2 = 48.0625 Factor a perfect square on the left side: (x + -0.25)(x + -0.25) = 48.0625 Calculate the square root of the right side: 6.932712312 Break this problem into two subproblems by setting (x + -0.25) equal to 6.932712312 and -6.932712312.Subproblem 1
x + -0.25 = 6.932712312 Simplifying x + -0.25 = 6.932712312 Reorder the terms: -0.25 + x = 6.932712312 Solving -0.25 + x = 6.932712312 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.25' to each side of the equation. -0.25 + 0.25 + x = 6.932712312 + 0.25 Combine like terms: -0.25 + 0.25 = 0.00 0.00 + x = 6.932712312 + 0.25 x = 6.932712312 + 0.25 Combine like terms: 6.932712312 + 0.25 = 7.182712312 x = 7.182712312 Simplifying x = 7.182712312Subproblem 2
x + -0.25 = -6.932712312 Simplifying x + -0.25 = -6.932712312 Reorder the terms: -0.25 + x = -6.932712312 Solving -0.25 + x = -6.932712312 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.25' to each side of the equation. -0.25 + 0.25 + x = -6.932712312 + 0.25 Combine like terms: -0.25 + 0.25 = 0.00 0.00 + x = -6.932712312 + 0.25 x = -6.932712312 + 0.25 Combine like terms: -6.932712312 + 0.25 = -6.682712312 x = -6.682712312 Simplifying x = -6.682712312Solution
The solution to the problem is based on the solutions from the subproblems. x = {7.182712312, -6.682712312}
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