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Simplifying 0 = 15x + x2 + 4 Reorder the terms: 0 = 4 + 15x + x2 Solving 0 = 4 + 15x + x2 Solving for variable 'x'. Combine like terms: 0 + -4 = -4 -4 + -15x + -1x2 = 4 + 15x + x2 + -4 + -15x + -1x2 Reorder the terms: -4 + -15x + -1x2 = 4 + -4 + 15x + -15x + x2 + -1x2 Combine like terms: 4 + -4 = 0 -4 + -15x + -1x2 = 0 + 15x + -15x + x2 + -1x2 -4 + -15x + -1x2 = 15x + -15x + x2 + -1x2 Combine like terms: 15x + -15x = 0 -4 + -15x + -1x2 = 0 + x2 + -1x2 -4 + -15x + -1x2 = x2 + -1x2 Combine like terms: x2 + -1x2 = 0 -4 + -15x + -1x2 = 0 Factor out the Greatest Common Factor (GCF), '-1'. -1(4 + 15x + x2) = 0 Ignore the factor -1.Subproblem 1
Set the factor '(4 + 15x + x2)' equal to zero and attempt to solve: Simplifying 4 + 15x + x2 = 0 Solving 4 + 15x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '-4' to each side of the equation. 4 + 15x + -4 + x2 = 0 + -4 Reorder the terms: 4 + -4 + 15x + x2 = 0 + -4 Combine like terms: 4 + -4 = 0 0 + 15x + x2 = 0 + -4 15x + x2 = 0 + -4 Combine like terms: 0 + -4 = -4 15x + x2 = -4 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 = -4 + 56.25 Reorder the terms: 56.25 + 15x + x2 = -4 + 56.25 Combine like terms: -4 + 56.25 = 52.25 56.25 + 15x + x2 = 52.25 Factor a perfect square on the left side: (x + 7.5)(x + 7.5) = 52.25 Calculate the square root of the right side: 7.228416147 Break this problem into two subproblems by setting (x + 7.5) equal to 7.228416147 and -7.228416147.Subproblem 1
x + 7.5 = 7.228416147 Simplifying x + 7.5 = 7.228416147 Reorder the terms: 7.5 + x = 7.228416147 Solving 7.5 + x = 7.228416147 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 = 7.228416147 + -7.5 Combine like terms: 7.5 + -7.5 = 0.0 0.0 + x = 7.228416147 + -7.5 x = 7.228416147 + -7.5 Combine like terms: 7.228416147 + -7.5 = -0.271583853 x = -0.271583853 Simplifying x = -0.271583853Subproblem 2
x + 7.5 = -7.228416147 Simplifying x + 7.5 = -7.228416147 Reorder the terms: 7.5 + x = -7.228416147 Solving 7.5 + x = -7.228416147 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 = -7.228416147 + -7.5 Combine like terms: 7.5 + -7.5 = 0.0 0.0 + x = -7.228416147 + -7.5 x = -7.228416147 + -7.5 Combine like terms: -7.228416147 + -7.5 = -14.728416147 x = -14.728416147 Simplifying x = -14.728416147Solution
The solution to the problem is based on the solutions from the subproblems. x = {-0.271583853, -14.728416147}Solution
x = {-0.271583853, -14.728416147}
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