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Simplifying (10x + 4)(x + -5) = 4 Reorder the terms: (4 + 10x)(x + -5) = 4 Reorder the terms: (4 + 10x)(-5 + x) = 4 Multiply (4 + 10x) * (-5 + x) (4(-5 + x) + 10x * (-5 + x)) = 4 ((-5 * 4 + x * 4) + 10x * (-5 + x)) = 4 ((-20 + 4x) + 10x * (-5 + x)) = 4 (-20 + 4x + (-5 * 10x + x * 10x)) = 4 (-20 + 4x + (-50x + 10x2)) = 4 Combine like terms: 4x + -50x = -46x (-20 + -46x + 10x2) = 4 Solving -20 + -46x + 10x2 = 4 Solving for variable 'x'. Reorder the terms: -20 + -4 + -46x + 10x2 = 4 + -4 Combine like terms: -20 + -4 = -24 -24 + -46x + 10x2 = 4 + -4 Combine like terms: 4 + -4 = 0 -24 + -46x + 10x2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(-12 + -23x + 5x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-12 + -23x + 5x2)' equal to zero and attempt to solve: Simplifying -12 + -23x + 5x2 = 0 Solving -12 + -23x + 5x2 = 0 Begin completing the square. Divide all terms by 5 the coefficient of the squared term: Divide each side by '5'. -2.4 + -4.6x + x2 = 0 Move the constant term to the right: Add '2.4' to each side of the equation. -2.4 + -4.6x + 2.4 + x2 = 0 + 2.4 Reorder the terms: -2.4 + 2.4 + -4.6x + x2 = 0 + 2.4 Combine like terms: -2.4 + 2.4 = 0.0 0.0 + -4.6x + x2 = 0 + 2.4 -4.6x + x2 = 0 + 2.4 Combine like terms: 0 + 2.4 = 2.4 -4.6x + x2 = 2.4 The x term is -4.6x. Take half its coefficient (-2.3). Square it (5.29) and add it to both sides. Add '5.29' to each side of the equation. -4.6x + 5.29 + x2 = 2.4 + 5.29 Reorder the terms: 5.29 + -4.6x + x2 = 2.4 + 5.29 Combine like terms: 2.4 + 5.29 = 7.69 5.29 + -4.6x + x2 = 7.69 Factor a perfect square on the left side: (x + -2.3)(x + -2.3) = 7.69 Calculate the square root of the right side: 2.773084925 Break this problem into two subproblems by setting (x + -2.3) equal to 2.773084925 and -2.773084925.Subproblem 1
x + -2.3 = 2.773084925 Simplifying x + -2.3 = 2.773084925 Reorder the terms: -2.3 + x = 2.773084925 Solving -2.3 + x = 2.773084925 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.3' to each side of the equation. -2.3 + 2.3 + x = 2.773084925 + 2.3 Combine like terms: -2.3 + 2.3 = 0.0 0.0 + x = 2.773084925 + 2.3 x = 2.773084925 + 2.3 Combine like terms: 2.773084925 + 2.3 = 5.073084925 x = 5.073084925 Simplifying x = 5.073084925Subproblem 2
x + -2.3 = -2.773084925 Simplifying x + -2.3 = -2.773084925 Reorder the terms: -2.3 + x = -2.773084925 Solving -2.3 + x = -2.773084925 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.3' to each side of the equation. -2.3 + 2.3 + x = -2.773084925 + 2.3 Combine like terms: -2.3 + 2.3 = 0.0 0.0 + x = -2.773084925 + 2.3 x = -2.773084925 + 2.3 Combine like terms: -2.773084925 + 2.3 = -0.473084925 x = -0.473084925 Simplifying x = -0.473084925Solution
The solution to the problem is based on the solutions from the subproblems. x = {5.073084925, -0.473084925}Solution
x = {5.073084925, -0.473084925}
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