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Simplifying -5(5x2 + -1x + -28) = 0 Reorder the terms: -5(-28 + -1x + 5x2) = 0 (-28 * -5 + -1x * -5 + 5x2 * -5) = 0 (140 + 5x + -25x2) = 0 Solving 140 + 5x + -25x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '5'. 5(28 + x + -5x2) = 0 Ignore the factor 5.Subproblem 1
Set the factor '(28 + x + -5x2)' equal to zero and attempt to solve: Simplifying 28 + x + -5x2 = 0 Solving 28 + x + -5x2 = 0 Begin completing the square. Divide all terms by -5 the coefficient of the squared term: Divide each side by '-5'. -5.6 + -0.2x + x2 = 0 Move the constant term to the right: Add '5.6' to each side of the equation. -5.6 + -0.2x + 5.6 + x2 = 0 + 5.6 Reorder the terms: -5.6 + 5.6 + -0.2x + x2 = 0 + 5.6 Combine like terms: -5.6 + 5.6 = 0.0 0.0 + -0.2x + x2 = 0 + 5.6 -0.2x + x2 = 0 + 5.6 Combine like terms: 0 + 5.6 = 5.6 -0.2x + x2 = 5.6 The x term is x. Take half its coefficient (0.5). Square it (0.25) and add it to both sides. Add '0.25' to each side of the equation. -0.2x + 0.25 + x2 = 5.6 + 0.25 Reorder the terms: 0.25 + -0.2x + x2 = 5.6 + 0.25 Combine like terms: 5.6 + 0.25 = 5.85 0.25 + -0.2x + x2 = 5.85 Factor a perfect square on the left side: (x + 0.5)(x + 0.5) = 5.85 Calculate the square root of the right side: 2.418677324 Break this problem into two subproblems by setting (x + 0.5) equal to 2.418677324 and -2.418677324.Subproblem 1
x + 0.5 = 2.418677324 Simplifying x + 0.5 = 2.418677324 Reorder the terms: 0.5 + x = 2.418677324 Solving 0.5 + x = 2.418677324 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.5' to each side of the equation. 0.5 + -0.5 + x = 2.418677324 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x = 2.418677324 + -0.5 x = 2.418677324 + -0.5 Combine like terms: 2.418677324 + -0.5 = 1.918677324 x = 1.918677324 Simplifying x = 1.918677324Subproblem 2
x + 0.5 = -2.418677324 Simplifying x + 0.5 = -2.418677324 Reorder the terms: 0.5 + x = -2.418677324 Solving 0.5 + x = -2.418677324 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.5' to each side of the equation. 0.5 + -0.5 + x = -2.418677324 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x = -2.418677324 + -0.5 x = -2.418677324 + -0.5 Combine like terms: -2.418677324 + -0.5 = -2.918677324 x = -2.918677324 Simplifying x = -2.918677324Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.918677324, -2.918677324}Solution
x = {1.918677324, -2.918677324}
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