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Simplifying x2 + -12.5x + -24 = 0 Reorder the terms: -24 + -12.5x + x2 = 0 Solving -24 + -12.5x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '24' to each side of the equation. -24 + -12.5x + 24 + x2 = 0 + 24 Reorder the terms: -24 + 24 + -12.5x + x2 = 0 + 24 Combine like terms: -24 + 24 = 0 0 + -12.5x + x2 = 0 + 24 -12.5x + x2 = 0 + 24 Combine like terms: 0 + 24 = 24 -12.5x + x2 = 24 The x term is -12.5x. Take half its coefficient (-6.25). Square it (39.0625) and add it to both sides. Add '39.0625' to each side of the equation. -12.5x + 39.0625 + x2 = 24 + 39.0625 Reorder the terms: 39.0625 + -12.5x + x2 = 24 + 39.0625 Combine like terms: 24 + 39.0625 = 63.0625 39.0625 + -12.5x + x2 = 63.0625 Factor a perfect square on the left side: (x + -6.25)(x + -6.25) = 63.0625 Calculate the square root of the right side: 7.941190087 Break this problem into two subproblems by setting (x + -6.25) equal to 7.941190087 and -7.941190087.Subproblem 1
x + -6.25 = 7.941190087 Simplifying x + -6.25 = 7.941190087 Reorder the terms: -6.25 + x = 7.941190087 Solving -6.25 + x = 7.941190087 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '6.25' to each side of the equation. -6.25 + 6.25 + x = 7.941190087 + 6.25 Combine like terms: -6.25 + 6.25 = 0.00 0.00 + x = 7.941190087 + 6.25 x = 7.941190087 + 6.25 Combine like terms: 7.941190087 + 6.25 = 14.191190087 x = 14.191190087 Simplifying x = 14.191190087Subproblem 2
x + -6.25 = -7.941190087 Simplifying x + -6.25 = -7.941190087 Reorder the terms: -6.25 + x = -7.941190087 Solving -6.25 + x = -7.941190087 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '6.25' to each side of the equation. -6.25 + 6.25 + x = -7.941190087 + 6.25 Combine like terms: -6.25 + 6.25 = 0.00 0.00 + x = -7.941190087 + 6.25 x = -7.941190087 + 6.25 Combine like terms: -7.941190087 + 6.25 = -1.691190087 x = -1.691190087 Simplifying x = -1.691190087Solution
The solution to the problem is based on the solutions from the subproblems. x = {14.191190087, -1.691190087}
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