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Simplifying -4x2 + 23 = -4x Reorder the terms: 23 + -4x2 = -4x Solving 23 + -4x2 = -4x Solving for variable 'x'. Reorder the terms: 23 + 4x + -4x2 = -4x + 4x Combine like terms: -4x + 4x = 0 23 + 4x + -4x2 = 0 Begin completing the square. Divide all terms by -4 the coefficient of the squared term: Divide each side by '-4'. -5.75 + -1x + x2 = 0 Move the constant term to the right: Add '5.75' to each side of the equation. -5.75 + -1x + 5.75 + x2 = 0 + 5.75 Reorder the terms: -5.75 + 5.75 + -1x + x2 = 0 + 5.75 Combine like terms: -5.75 + 5.75 = 0.00 0.00 + -1x + x2 = 0 + 5.75 -1x + x2 = 0 + 5.75 Combine like terms: 0 + 5.75 = 5.75 -1x + x2 = 5.75 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 = 5.75 + 0.25 Reorder the terms: 0.25 + -1x + x2 = 5.75 + 0.25 Combine like terms: 5.75 + 0.25 = 6 0.25 + -1x + x2 = 6 Factor a perfect square on the left side: (x + -0.5)(x + -0.5) = 6 Calculate the square root of the right side: 2.449489743 Break this problem into two subproblems by setting (x + -0.5) equal to 2.449489743 and -2.449489743.Subproblem 1
x + -0.5 = 2.449489743 Simplifying x + -0.5 = 2.449489743 Reorder the terms: -0.5 + x = 2.449489743 Solving -0.5 + x = 2.449489743 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 = 2.449489743 + 0.5 Combine like terms: -0.5 + 0.5 = 0.0 0.0 + x = 2.449489743 + 0.5 x = 2.449489743 + 0.5 Combine like terms: 2.449489743 + 0.5 = 2.949489743 x = 2.949489743 Simplifying x = 2.949489743Subproblem 2
x + -0.5 = -2.449489743 Simplifying x + -0.5 = -2.449489743 Reorder the terms: -0.5 + x = -2.449489743 Solving -0.5 + x = -2.449489743 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 = -2.449489743 + 0.5 Combine like terms: -0.5 + 0.5 = 0.0 0.0 + x = -2.449489743 + 0.5 x = -2.449489743 + 0.5 Combine like terms: -2.449489743 + 0.5 = -1.949489743 x = -1.949489743 Simplifying x = -1.949489743Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.949489743, -1.949489743}
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