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Simplifying 0 = 15 + -5x2 + -15x Reorder the terms: 0 = 15 + -15x + -5x2 Solving 0 = 15 + -15x + -5x2 Solving for variable 'x'. Combine like terms: 0 + -15 = -15 -15 + 15x + 5x2 = 15 + -15x + -5x2 + -15 + 15x + 5x2 Reorder the terms: -15 + 15x + 5x2 = 15 + -15 + -15x + 15x + -5x2 + 5x2 Combine like terms: 15 + -15 = 0 -15 + 15x + 5x2 = 0 + -15x + 15x + -5x2 + 5x2 -15 + 15x + 5x2 = -15x + 15x + -5x2 + 5x2 Combine like terms: -15x + 15x = 0 -15 + 15x + 5x2 = 0 + -5x2 + 5x2 -15 + 15x + 5x2 = -5x2 + 5x2 Combine like terms: -5x2 + 5x2 = 0 -15 + 15x + 5x2 = 0 Factor out the Greatest Common Factor (GCF), '5'. 5(-3 + 3x + x2) = 0 Ignore the factor 5.Subproblem 1
Set the factor '(-3 + 3x + x2)' equal to zero and attempt to solve: Simplifying -3 + 3x + x2 = 0 Solving -3 + 3x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '3' to each side of the equation. -3 + 3x + 3 + x2 = 0 + 3 Reorder the terms: -3 + 3 + 3x + x2 = 0 + 3 Combine like terms: -3 + 3 = 0 0 + 3x + x2 = 0 + 3 3x + x2 = 0 + 3 Combine like terms: 0 + 3 = 3 3x + x2 = 3 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 = 3 + 2.25 Reorder the terms: 2.25 + 3x + x2 = 3 + 2.25 Combine like terms: 3 + 2.25 = 5.25 2.25 + 3x + x2 = 5.25 Factor a perfect square on the left side: (x + 1.5)(x + 1.5) = 5.25 Calculate the square root of the right side: 2.291287847 Break this problem into two subproblems by setting (x + 1.5) equal to 2.291287847 and -2.291287847.Subproblem 1
x + 1.5 = 2.291287847 Simplifying x + 1.5 = 2.291287847 Reorder the terms: 1.5 + x = 2.291287847 Solving 1.5 + x = 2.291287847 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 = 2.291287847 + -1.5 Combine like terms: 1.5 + -1.5 = 0.0 0.0 + x = 2.291287847 + -1.5 x = 2.291287847 + -1.5 Combine like terms: 2.291287847 + -1.5 = 0.791287847 x = 0.791287847 Simplifying x = 0.791287847Subproblem 2
x + 1.5 = -2.291287847 Simplifying x + 1.5 = -2.291287847 Reorder the terms: 1.5 + x = -2.291287847 Solving 1.5 + x = -2.291287847 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 = -2.291287847 + -1.5 Combine like terms: 1.5 + -1.5 = 0.0 0.0 + x = -2.291287847 + -1.5 x = -2.291287847 + -1.5 Combine like terms: -2.291287847 + -1.5 = -3.791287847 x = -3.791287847 Simplifying x = -3.791287847Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.791287847, -3.791287847}Solution
x = {0.791287847, -3.791287847}
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