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Simplifying 2(x2 + 15x + -22) = 0 Reorder the terms: 2(-22 + 15x + x2) = 0 (-22 * 2 + 15x * 2 + x2 * 2) = 0 (-44 + 30x + 2x2) = 0 Solving -44 + 30x + 2x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '2'. 2(-22 + 15x + x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-22 + 15x + x2)' equal to zero and attempt to solve: Simplifying -22 + 15x + x2 = 0 Solving -22 + 15x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '22' to each side of the equation. -22 + 15x + 22 + x2 = 0 + 22 Reorder the terms: -22 + 22 + 15x + x2 = 0 + 22 Combine like terms: -22 + 22 = 0 0 + 15x + x2 = 0 + 22 15x + x2 = 0 + 22 Combine like terms: 0 + 22 = 22 15x + x2 = 22 The x term is 15x. Take half its coefficient (7.5). Square it (56.25) and add it to both sides. Add '56.25' to each side of the equation. 15x + 56.25 + x2 = 22 + 56.25 Reorder the terms: 56.25 + 15x + x2 = 22 + 56.25 Combine like terms: 22 + 56.25 = 78.25 56.25 + 15x + x2 = 78.25 Factor a perfect square on the left side: (x + 7.5)(x + 7.5) = 78.25 Calculate the square root of the right side: 8.845903006 Break this problem into two subproblems by setting (x + 7.5) equal to 8.845903006 and -8.845903006.Subproblem 1
x + 7.5 = 8.845903006 Simplifying x + 7.5 = 8.845903006 Reorder the terms: 7.5 + x = 8.845903006 Solving 7.5 + x = 8.845903006 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-7.5' to each side of the equation. 7.5 + -7.5 + x = 8.845903006 + -7.5 Combine like terms: 7.5 + -7.5 = 0.0 0.0 + x = 8.845903006 + -7.5 x = 8.845903006 + -7.5 Combine like terms: 8.845903006 + -7.5 = 1.345903006 x = 1.345903006 Simplifying x = 1.345903006Subproblem 2
x + 7.5 = -8.845903006 Simplifying x + 7.5 = -8.845903006 Reorder the terms: 7.5 + x = -8.845903006 Solving 7.5 + x = -8.845903006 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-7.5' to each side of the equation. 7.5 + -7.5 + x = -8.845903006 + -7.5 Combine like terms: 7.5 + -7.5 = 0.0 0.0 + x = -8.845903006 + -7.5 x = -8.845903006 + -7.5 Combine like terms: -8.845903006 + -7.5 = -16.345903006 x = -16.345903006 Simplifying x = -16.345903006Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.345903006, -16.345903006}Solution
x = {1.345903006, -16.345903006}
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