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Simplifying 2x2 + 6x + -19 = 87 Reorder the terms: -19 + 6x + 2x2 = 87 Solving -19 + 6x + 2x2 = 87 Solving for variable 'x'. Reorder the terms: -19 + -87 + 6x + 2x2 = 87 + -87 Combine like terms: -19 + -87 = -106 -106 + 6x + 2x2 = 87 + -87 Combine like terms: 87 + -87 = 0 -106 + 6x + 2x2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(-53 + 3x + x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-53 + 3x + x2)' equal to zero and attempt to solve: Simplifying -53 + 3x + x2 = 0 Solving -53 + 3x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '53' to each side of the equation. -53 + 3x + 53 + x2 = 0 + 53 Reorder the terms: -53 + 53 + 3x + x2 = 0 + 53 Combine like terms: -53 + 53 = 0 0 + 3x + x2 = 0 + 53 3x + x2 = 0 + 53 Combine like terms: 0 + 53 = 53 3x + x2 = 53 The x term is 3x. Take half its coefficient (1.5). Square it (2.25) and add it to both sides. Add '2.25' to each side of the equation. 3x + 2.25 + x2 = 53 + 2.25 Reorder the terms: 2.25 + 3x + x2 = 53 + 2.25 Combine like terms: 53 + 2.25 = 55.25 2.25 + 3x + x2 = 55.25 Factor a perfect square on the left side: (x + 1.5)(x + 1.5) = 55.25 Calculate the square root of the right side: 7.433034374 Break this problem into two subproblems by setting (x + 1.5) equal to 7.433034374 and -7.433034374.Subproblem 1
x + 1.5 = 7.433034374 Simplifying x + 1.5 = 7.433034374 Reorder the terms: 1.5 + x = 7.433034374 Solving 1.5 + x = 7.433034374 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.5' to each side of the equation. 1.5 + -1.5 + x = 7.433034374 + -1.5 Combine like terms: 1.5 + -1.5 = 0.0 0.0 + x = 7.433034374 + -1.5 x = 7.433034374 + -1.5 Combine like terms: 7.433034374 + -1.5 = 5.933034374 x = 5.933034374 Simplifying x = 5.933034374Subproblem 2
x + 1.5 = -7.433034374 Simplifying x + 1.5 = -7.433034374 Reorder the terms: 1.5 + x = -7.433034374 Solving 1.5 + x = -7.433034374 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.5' to each side of the equation. 1.5 + -1.5 + x = -7.433034374 + -1.5 Combine like terms: 1.5 + -1.5 = 0.0 0.0 + x = -7.433034374 + -1.5 x = -7.433034374 + -1.5 Combine like terms: -7.433034374 + -1.5 = -8.933034374 x = -8.933034374 Simplifying x = -8.933034374Solution
The solution to the problem is based on the solutions from the subproblems. x = {5.933034374, -8.933034374}Solution
x = {5.933034374, -8.933034374}
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