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Simplifying 2x2 + -2x + -1 = 24 Reorder the terms: -1 + -2x + 2x2 = 24 Solving -1 + -2x + 2x2 = 24 Solving for variable 'x'. Reorder the terms: -1 + -24 + -2x + 2x2 = 24 + -24 Combine like terms: -1 + -24 = -25 -25 + -2x + 2x2 = 24 + -24 Combine like terms: 24 + -24 = 0 -25 + -2x + 2x2 = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. -12.5 + -1x + x2 = 0 Move the constant term to the right: Add '12.5' to each side of the equation. -12.5 + -1x + 12.5 + x2 = 0 + 12.5 Reorder the terms: -12.5 + 12.5 + -1x + x2 = 0 + 12.5 Combine like terms: -12.5 + 12.5 = 0.0 0.0 + -1x + x2 = 0 + 12.5 -1x + x2 = 0 + 12.5 Combine like terms: 0 + 12.5 = 12.5 -1x + x2 = 12.5 The x term is -1x. Take half its coefficient (-0.5). Square it (0.25) and add it to both sides. Add '0.25' to each side of the equation. -1x + 0.25 + x2 = 12.5 + 0.25 Reorder the terms: 0.25 + -1x + x2 = 12.5 + 0.25 Combine like terms: 12.5 + 0.25 = 12.75 0.25 + -1x + x2 = 12.75 Factor a perfect square on the left side: (x + -0.5)(x + -0.5) = 12.75 Calculate the square root of the right side: 3.570714214 Break this problem into two subproblems by setting (x + -0.5) equal to 3.570714214 and -3.570714214.Subproblem 1
x + -0.5 = 3.570714214 Simplifying x + -0.5 = 3.570714214 Reorder the terms: -0.5 + x = 3.570714214 Solving -0.5 + x = 3.570714214 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.5' to each side of the equation. -0.5 + 0.5 + x = 3.570714214 + 0.5 Combine like terms: -0.5 + 0.5 = 0.0 0.0 + x = 3.570714214 + 0.5 x = 3.570714214 + 0.5 Combine like terms: 3.570714214 + 0.5 = 4.070714214 x = 4.070714214 Simplifying x = 4.070714214Subproblem 2
x + -0.5 = -3.570714214 Simplifying x + -0.5 = -3.570714214 Reorder the terms: -0.5 + x = -3.570714214 Solving -0.5 + x = -3.570714214 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.5' to each side of the equation. -0.5 + 0.5 + x = -3.570714214 + 0.5 Combine like terms: -0.5 + 0.5 = 0.0 0.0 + x = -3.570714214 + 0.5 x = -3.570714214 + 0.5 Combine like terms: -3.570714214 + 0.5 = -3.070714214 x = -3.070714214 Simplifying x = -3.070714214Solution
The solution to the problem is based on the solutions from the subproblems. x = {4.070714214, -3.070714214}
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