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Simplifying 5x(5x + -5) = 30 Reorder the terms: 5x(-5 + 5x) = 30 (-5 * 5x + 5x * 5x) = 30 (-25x + 25x2) = 30 Solving -25x + 25x2 = 30 Solving for variable 'x'. Reorder the terms: -30 + -25x + 25x2 = 30 + -30 Combine like terms: 30 + -30 = 0 -30 + -25x + 25x2 = 0 Factor out the Greatest Common Factor (GCF), '5'. 5(-6 + -5x + 5x2) = 0 Ignore the factor 5.Subproblem 1
Set the factor '(-6 + -5x + 5x2)' equal to zero and attempt to solve: Simplifying -6 + -5x + 5x2 = 0 Solving -6 + -5x + 5x2 = 0 Begin completing the square. Divide all terms by 5 the coefficient of the squared term: Divide each side by '5'. -1.2 + -1x + x2 = 0 Move the constant term to the right: Add '1.2' to each side of the equation. -1.2 + -1x + 1.2 + x2 = 0 + 1.2 Reorder the terms: -1.2 + 1.2 + -1x + x2 = 0 + 1.2 Combine like terms: -1.2 + 1.2 = 0.0 0.0 + -1x + x2 = 0 + 1.2 -1x + x2 = 0 + 1.2 Combine like terms: 0 + 1.2 = 1.2 -1x + x2 = 1.2 The x term is -1x. 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. -1x + 0.25 + x2 = 1.2 + 0.25 Reorder the terms: 0.25 + -1x + x2 = 1.2 + 0.25 Combine like terms: 1.2 + 0.25 = 1.45 0.25 + -1x + x2 = 1.45 Factor a perfect square on the left side: (x + -0.5)(x + -0.5) = 1.45 Calculate the square root of the right side: 1.204159458 Break this problem into two subproblems by setting (x + -0.5) equal to 1.204159458 and -1.204159458.Subproblem 1
x + -0.5 = 1.204159458 Simplifying x + -0.5 = 1.204159458 Reorder the terms: -0.5 + x = 1.204159458 Solving -0.5 + x = 1.204159458 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 = 1.204159458 + 0.5 Combine like terms: -0.5 + 0.5 = 0.0 0.0 + x = 1.204159458 + 0.5 x = 1.204159458 + 0.5 Combine like terms: 1.204159458 + 0.5 = 1.704159458 x = 1.704159458 Simplifying x = 1.704159458Subproblem 2
x + -0.5 = -1.204159458 Simplifying x + -0.5 = -1.204159458 Reorder the terms: -0.5 + x = -1.204159458 Solving -0.5 + x = -1.204159458 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 = -1.204159458 + 0.5 Combine like terms: -0.5 + 0.5 = 0.0 0.0 + x = -1.204159458 + 0.5 x = -1.204159458 + 0.5 Combine like terms: -1.204159458 + 0.5 = -0.704159458 x = -0.704159458 Simplifying x = -0.704159458Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.704159458, -0.704159458}Solution
x = {1.704159458, -0.704159458}
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