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Simplifying (4x + 5)(x + -3) = 8 Reorder the terms: (5 + 4x)(x + -3) = 8 Reorder the terms: (5 + 4x)(-3 + x) = 8 Multiply (5 + 4x) * (-3 + x) (5(-3 + x) + 4x * (-3 + x)) = 8 ((-3 * 5 + x * 5) + 4x * (-3 + x)) = 8 ((-15 + 5x) + 4x * (-3 + x)) = 8 (-15 + 5x + (-3 * 4x + x * 4x)) = 8 (-15 + 5x + (-12x + 4x2)) = 8 Combine like terms: 5x + -12x = -7x (-15 + -7x + 4x2) = 8 Solving -15 + -7x + 4x2 = 8 Solving for variable 'x'. Reorder the terms: -15 + -8 + -7x + 4x2 = 8 + -8 Combine like terms: -15 + -8 = -23 -23 + -7x + 4x2 = 8 + -8 Combine like terms: 8 + -8 = 0 -23 + -7x + 4x2 = 0 Begin completing the square. Divide all terms by 4 the coefficient of the squared term: Divide each side by '4'. -5.75 + -1.75x + x2 = 0 Move the constant term to the right: Add '5.75' to each side of the equation. -5.75 + -1.75x + 5.75 + x2 = 0 + 5.75 Reorder the terms: -5.75 + 5.75 + -1.75x + x2 = 0 + 5.75 Combine like terms: -5.75 + 5.75 = 0.00 0.00 + -1.75x + x2 = 0 + 5.75 -1.75x + x2 = 0 + 5.75 Combine like terms: 0 + 5.75 = 5.75 -1.75x + x2 = 5.75 The x term is -1.75x. Take half its coefficient (-0.875). Square it (0.765625) and add it to both sides. Add '0.765625' to each side of the equation. -1.75x + 0.765625 + x2 = 5.75 + 0.765625 Reorder the terms: 0.765625 + -1.75x + x2 = 5.75 + 0.765625 Combine like terms: 5.75 + 0.765625 = 6.515625 0.765625 + -1.75x + x2 = 6.515625 Factor a perfect square on the left side: (x + -0.875)(x + -0.875) = 6.515625 Calculate the square root of the right side: 2.552572232 Break this problem into two subproblems by setting (x + -0.875) equal to 2.552572232 and -2.552572232.Subproblem 1
x + -0.875 = 2.552572232 Simplifying x + -0.875 = 2.552572232 Reorder the terms: -0.875 + x = 2.552572232 Solving -0.875 + x = 2.552572232 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.875' to each side of the equation. -0.875 + 0.875 + x = 2.552572232 + 0.875 Combine like terms: -0.875 + 0.875 = 0.000 0.000 + x = 2.552572232 + 0.875 x = 2.552572232 + 0.875 Combine like terms: 2.552572232 + 0.875 = 3.427572232 x = 3.427572232 Simplifying x = 3.427572232Subproblem 2
x + -0.875 = -2.552572232 Simplifying x + -0.875 = -2.552572232 Reorder the terms: -0.875 + x = -2.552572232 Solving -0.875 + x = -2.552572232 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.875' to each side of the equation. -0.875 + 0.875 + x = -2.552572232 + 0.875 Combine like terms: -0.875 + 0.875 = 0.000 0.000 + x = -2.552572232 + 0.875 x = -2.552572232 + 0.875 Combine like terms: -2.552572232 + 0.875 = -1.677572232 x = -1.677572232 Simplifying x = -1.677572232Solution
The solution to the problem is based on the solutions from the subproblems. x = {3.427572232, -1.677572232}
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