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Simplifying (5x2 + 6x + 1) + -1(4x2 + -9x) = 0 Reorder the terms: (1 + 6x + 5x2) + -1(4x2 + -9x) = 0 Remove parenthesis around (1 + 6x + 5x2) 1 + 6x + 5x2 + -1(4x2 + -9x) = 0 Reorder the terms: 1 + 6x + 5x2 + -1(-9x + 4x2) = 0 1 + 6x + 5x2 + (-9x * -1 + 4x2 * -1) = 0 1 + 6x + 5x2 + (9x + -4x2) = 0 Reorder the terms: 1 + 6x + 9x + 5x2 + -4x2 = 0 Combine like terms: 6x + 9x = 15x 1 + 15x + 5x2 + -4x2 = 0 Combine like terms: 5x2 + -4x2 = 1x2 1 + 15x + 1x2 = 0 Solving 1 + 15x + 1x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '-1' to each side of the equation. 1 + 15x + -1 + x2 = 0 + -1 Reorder the terms: 1 + -1 + 15x + x2 = 0 + -1 Combine like terms: 1 + -1 = 0 0 + 15x + x2 = 0 + -1 15x + x2 = 0 + -1 Combine like terms: 0 + -1 = -1 15x + x2 = -1 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 = -1 + 56.25 Reorder the terms: 56.25 + 15x + x2 = -1 + 56.25 Combine like terms: -1 + 56.25 = 55.25 56.25 + 15x + x2 = 55.25 Factor a perfect square on the left side: (x + 7.5)(x + 7.5) = 55.25 Calculate the square root of the right side: 7.433034374 Break this problem into two subproblems by setting (x + 7.5) equal to 7.433034374 and -7.433034374.Subproblem 1
x + 7.5 = 7.433034374 Simplifying x + 7.5 = 7.433034374 Reorder the terms: 7.5 + x = 7.433034374 Solving 7.5 + x = 7.433034374 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 = 7.433034374 + -7.5 Combine like terms: 7.5 + -7.5 = 0.0 0.0 + x = 7.433034374 + -7.5 x = 7.433034374 + -7.5 Combine like terms: 7.433034374 + -7.5 = -0.066965626 x = -0.066965626 Simplifying x = -0.066965626Subproblem 2
x + 7.5 = -7.433034374 Simplifying x + 7.5 = -7.433034374 Reorder the terms: 7.5 + x = -7.433034374 Solving 7.5 + x = -7.433034374 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 = -7.433034374 + -7.5 Combine like terms: 7.5 + -7.5 = 0.0 0.0 + x = -7.433034374 + -7.5 x = -7.433034374 + -7.5 Combine like terms: -7.433034374 + -7.5 = -14.933034374 x = -14.933034374 Simplifying x = -14.933034374Solution
The solution to the problem is based on the solutions from the subproblems. x = {-0.066965626, -14.933034374}
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