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Simplifying (2x2 + 6x + -5)(4x) = 0 Reorder the terms: (-5 + 6x + 2x2)(4x) = 0 Remove parenthesis around (4x) (-5 + 6x + 2x2) * 4x = 0 Reorder the terms for easier multiplication: 4x(-5 + 6x + 2x2) = 0 (-5 * 4x + 6x * 4x + 2x2 * 4x) = 0 (-20x + 24x2 + 8x3) = 0 Solving -20x + 24x2 + 8x3 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '4x'. 4x(-5 + 6x + 2x2) = 0 Ignore the factor 4.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 + 2x2)' equal to zero and attempt to solve: Simplifying -5 + 6x + 2x2 = 0 Solving -5 + 6x + 2x2 = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. -2.5 + 3x + x2 = 0 Move the constant term to the right: Add '2.5' to each side of the equation. -2.5 + 3x + 2.5 + x2 = 0 + 2.5 Reorder the terms: -2.5 + 2.5 + 3x + x2 = 0 + 2.5 Combine like terms: -2.5 + 2.5 = 0.0 0.0 + 3x + x2 = 0 + 2.5 3x + x2 = 0 + 2.5 Combine like terms: 0 + 2.5 = 2.5 3x + x2 = 2.5 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 = 2.5 + 2.25 Reorder the terms: 2.25 + 3x + x2 = 2.5 + 2.25 Combine like terms: 2.5 + 2.25 = 4.75 2.25 + 3x + x2 = 4.75 Factor a perfect square on the left side: (x + 1.5)(x + 1.5) = 4.75 Calculate the square root of the right side: 2.179449472 Break this problem into two subproblems by setting (x + 1.5) equal to 2.179449472 and -2.179449472.Subproblem 1
x + 1.5 = 2.179449472 Simplifying x + 1.5 = 2.179449472 Reorder the terms: 1.5 + x = 2.179449472 Solving 1.5 + x = 2.179449472 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 = 2.179449472 + -1.5 Combine like terms: 1.5 + -1.5 = 0.0 0.0 + x = 2.179449472 + -1.5 x = 2.179449472 + -1.5 Combine like terms: 2.179449472 + -1.5 = 0.679449472 x = 0.679449472 Simplifying x = 0.679449472Subproblem 2
x + 1.5 = -2.179449472 Simplifying x + 1.5 = -2.179449472 Reorder the terms: 1.5 + x = -2.179449472 Solving 1.5 + x = -2.179449472 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 = -2.179449472 + -1.5 Combine like terms: 1.5 + -1.5 = 0.0 0.0 + x = -2.179449472 + -1.5 x = -2.179449472 + -1.5 Combine like terms: -2.179449472 + -1.5 = -3.679449472 x = -3.679449472 Simplifying x = -3.679449472Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.679449472, -3.679449472}Solution
x = {0, 0.679449472, -3.679449472}
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