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Simplifying -1x2 = 15x + 30 Reorder the terms: -1x2 = 30 + 15x Solving -1x2 = 30 + 15x Solving for variable 'x'. Reorder the terms: -30 + -15x + -1x2 = 30 + 15x + -30 + -15x Reorder the terms: -30 + -15x + -1x2 = 30 + -30 + 15x + -15x Combine like terms: 30 + -30 = 0 -30 + -15x + -1x2 = 0 + 15x + -15x -30 + -15x + -1x2 = 15x + -15x Combine like terms: 15x + -15x = 0 -30 + -15x + -1x2 = 0 Factor out the Greatest Common Factor (GCF), '-1'. -1(30 + 15x + x2) = 0 Ignore the factor -1.Subproblem 1
Set the factor '(30 + 15x + x2)' equal to zero and attempt to solve: Simplifying 30 + 15x + x2 = 0 Solving 30 + 15x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '-30' to each side of the equation. 30 + 15x + -30 + x2 = 0 + -30 Reorder the terms: 30 + -30 + 15x + x2 = 0 + -30 Combine like terms: 30 + -30 = 0 0 + 15x + x2 = 0 + -30 15x + x2 = 0 + -30 Combine like terms: 0 + -30 = -30 15x + x2 = -30 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 = -30 + 56.25 Reorder the terms: 56.25 + 15x + x2 = -30 + 56.25 Combine like terms: -30 + 56.25 = 26.25 56.25 + 15x + x2 = 26.25 Factor a perfect square on the left side: (x + 7.5)(x + 7.5) = 26.25 Calculate the square root of the right side: 5.123475383 Break this problem into two subproblems by setting (x + 7.5) equal to 5.123475383 and -5.123475383.Subproblem 1
x + 7.5 = 5.123475383 Simplifying x + 7.5 = 5.123475383 Reorder the terms: 7.5 + x = 5.123475383 Solving 7.5 + x = 5.123475383 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 = 5.123475383 + -7.5 Combine like terms: 7.5 + -7.5 = 0.0 0.0 + x = 5.123475383 + -7.5 x = 5.123475383 + -7.5 Combine like terms: 5.123475383 + -7.5 = -2.376524617 x = -2.376524617 Simplifying x = -2.376524617Subproblem 2
x + 7.5 = -5.123475383 Simplifying x + 7.5 = -5.123475383 Reorder the terms: 7.5 + x = -5.123475383 Solving 7.5 + x = -5.123475383 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 = -5.123475383 + -7.5 Combine like terms: 7.5 + -7.5 = 0.0 0.0 + x = -5.123475383 + -7.5 x = -5.123475383 + -7.5 Combine like terms: -5.123475383 + -7.5 = -12.623475383 x = -12.623475383 Simplifying x = -12.623475383Solution
The solution to the problem is based on the solutions from the subproblems. x = {-2.376524617, -12.623475383}Solution
x = {-2.376524617, -12.623475383}
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