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Simplifying 5x2 + -25 + 10x = 0 Reorder the terms: -25 + 10x + 5x2 = 0 Solving -25 + 10x + 5x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '5'. 5(-5 + 2x + x2) = 0 Ignore the factor 5.Subproblem 1
Set the factor '(-5 + 2x + x2)' equal to zero and attempt to solve: Simplifying -5 + 2x + x2 = 0 Solving -5 + 2x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '5' to each side of the equation. -5 + 2x + 5 + x2 = 0 + 5 Reorder the terms: -5 + 5 + 2x + x2 = 0 + 5 Combine like terms: -5 + 5 = 0 0 + 2x + x2 = 0 + 5 2x + x2 = 0 + 5 Combine like terms: 0 + 5 = 5 2x + x2 = 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 = 5 + 1 Reorder the terms: 1 + 2x + x2 = 5 + 1 Combine like terms: 5 + 1 = 6 1 + 2x + x2 = 6 Factor a perfect square on the left side: (x + 1)(x + 1) = 6 Calculate the square root of the right side: 2.449489743 Break this problem into two subproblems by setting (x + 1) equal to 2.449489743 and -2.449489743.Subproblem 1
x + 1 = 2.449489743 Simplifying x + 1 = 2.449489743 Reorder the terms: 1 + x = 2.449489743 Solving 1 + x = 2.449489743 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 = 2.449489743 + -1 Combine like terms: 1 + -1 = 0 0 + x = 2.449489743 + -1 x = 2.449489743 + -1 Combine like terms: 2.449489743 + -1 = 1.449489743 x = 1.449489743 Simplifying x = 1.449489743Subproblem 2
x + 1 = -2.449489743 Simplifying x + 1 = -2.449489743 Reorder the terms: 1 + x = -2.449489743 Solving 1 + x = -2.449489743 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 = -2.449489743 + -1 Combine like terms: 1 + -1 = 0 0 + x = -2.449489743 + -1 x = -2.449489743 + -1 Combine like terms: -2.449489743 + -1 = -3.449489743 x = -3.449489743 Simplifying x = -3.449489743Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.449489743, -3.449489743}Solution
x = {1.449489743, -3.449489743}
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