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Simplifying 5x(5x2 + 6x + -5) = 0 Reorder the terms: 5x(-5 + 6x + 5x2) = 0 (-5 * 5x + 6x * 5x + 5x2 * 5x) = 0 (-25x + 30x2 + 25x3) = 0 Solving -25x + 30x2 + 25x3 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '5x'. 5x(-5 + 6x + 5x2) = 0 Ignore the factor 5.Subproblem 1
Set the factor 'x' equal to zero and attempt to solve: Simplifying x = 0 Solving x = 0 Move all terms containing x to the left, all other terms to the right. Simplifying x = 0Subproblem 2
Set the factor '(-5 + 6x + 5x2)' equal to zero and attempt to solve: Simplifying -5 + 6x + 5x2 = 0 Solving -5 + 6x + 5x2 = 0 Begin completing the square. Divide all terms by 5 the coefficient of the squared term: Divide each side by '5'. -1 + 1.2x + x2 = 0 Move the constant term to the right: Add '1' to each side of the equation. -1 + 1.2x + 1 + x2 = 0 + 1 Reorder the terms: -1 + 1 + 1.2x + x2 = 0 + 1 Combine like terms: -1 + 1 = 0 0 + 1.2x + x2 = 0 + 1 1.2x + x2 = 0 + 1 Combine like terms: 0 + 1 = 1 1.2x + x2 = 1 The x term is 1.2x. Take half its coefficient (0.6). Square it (0.36) and add it to both sides. Add '0.36' to each side of the equation. 1.2x + 0.36 + x2 = 1 + 0.36 Reorder the terms: 0.36 + 1.2x + x2 = 1 + 0.36 Combine like terms: 1 + 0.36 = 1.36 0.36 + 1.2x + x2 = 1.36 Factor a perfect square on the left side: (x + 0.6)(x + 0.6) = 1.36 Calculate the square root of the right side: 1.166190379 Break this problem into two subproblems by setting (x + 0.6) equal to 1.166190379 and -1.166190379.Subproblem 1
x + 0.6 = 1.166190379 Simplifying x + 0.6 = 1.166190379 Reorder the terms: 0.6 + x = 1.166190379 Solving 0.6 + x = 1.166190379 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.6' to each side of the equation. 0.6 + -0.6 + x = 1.166190379 + -0.6 Combine like terms: 0.6 + -0.6 = 0.0 0.0 + x = 1.166190379 + -0.6 x = 1.166190379 + -0.6 Combine like terms: 1.166190379 + -0.6 = 0.566190379 x = 0.566190379 Simplifying x = 0.566190379Subproblem 2
x + 0.6 = -1.166190379 Simplifying x + 0.6 = -1.166190379 Reorder the terms: 0.6 + x = -1.166190379 Solving 0.6 + x = -1.166190379 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.6' to each side of the equation. 0.6 + -0.6 + x = -1.166190379 + -0.6 Combine like terms: 0.6 + -0.6 = 0.0 0.0 + x = -1.166190379 + -0.6 x = -1.166190379 + -0.6 Combine like terms: -1.166190379 + -0.6 = -1.766190379 x = -1.766190379 Simplifying x = -1.766190379Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.566190379, -1.766190379}Solution
x = {0, 0.566190379, -1.766190379}
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