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Simplifying (4x + -3)(x + 5) = 10 Reorder the terms: (-3 + 4x)(x + 5) = 10 Reorder the terms: (-3 + 4x)(5 + x) = 10 Multiply (-3 + 4x) * (5 + x) (-3(5 + x) + 4x * (5 + x)) = 10 ((5 * -3 + x * -3) + 4x * (5 + x)) = 10 ((-15 + -3x) + 4x * (5 + x)) = 10 (-15 + -3x + (5 * 4x + x * 4x)) = 10 (-15 + -3x + (20x + 4x2)) = 10 Combine like terms: -3x + 20x = 17x (-15 + 17x + 4x2) = 10 Solving -15 + 17x + 4x2 = 10 Solving for variable 'x'. Reorder the terms: -15 + -10 + 17x + 4x2 = 10 + -10 Combine like terms: -15 + -10 = -25 -25 + 17x + 4x2 = 10 + -10 Combine like terms: 10 + -10 = 0 -25 + 17x + 4x2 = 0 Begin completing the square. Divide all terms by 4 the coefficient of the squared term: Divide each side by '4'. -6.25 + 4.25x + x2 = 0 Move the constant term to the right: Add '6.25' to each side of the equation. -6.25 + 4.25x + 6.25 + x2 = 0 + 6.25 Reorder the terms: -6.25 + 6.25 + 4.25x + x2 = 0 + 6.25 Combine like terms: -6.25 + 6.25 = 0.00 0.00 + 4.25x + x2 = 0 + 6.25 4.25x + x2 = 0 + 6.25 Combine like terms: 0 + 6.25 = 6.25 4.25x + x2 = 6.25 The x term is 4.25x. Take half its coefficient (2.125). Square it (4.515625) and add it to both sides. Add '4.515625' to each side of the equation. 4.25x + 4.515625 + x2 = 6.25 + 4.515625 Reorder the terms: 4.515625 + 4.25x + x2 = 6.25 + 4.515625 Combine like terms: 6.25 + 4.515625 = 10.765625 4.515625 + 4.25x + x2 = 10.765625 Factor a perfect square on the left side: (x + 2.125)(x + 2.125) = 10.765625 Calculate the square root of the right side: 3.281101187 Break this problem into two subproblems by setting (x + 2.125) equal to 3.281101187 and -3.281101187.Subproblem 1
x + 2.125 = 3.281101187 Simplifying x + 2.125 = 3.281101187 Reorder the terms: 2.125 + x = 3.281101187 Solving 2.125 + x = 3.281101187 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2.125' to each side of the equation. 2.125 + -2.125 + x = 3.281101187 + -2.125 Combine like terms: 2.125 + -2.125 = 0.000 0.000 + x = 3.281101187 + -2.125 x = 3.281101187 + -2.125 Combine like terms: 3.281101187 + -2.125 = 1.156101187 x = 1.156101187 Simplifying x = 1.156101187Subproblem 2
x + 2.125 = -3.281101187 Simplifying x + 2.125 = -3.281101187 Reorder the terms: 2.125 + x = -3.281101187 Solving 2.125 + x = -3.281101187 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2.125' to each side of the equation. 2.125 + -2.125 + x = -3.281101187 + -2.125 Combine like terms: 2.125 + -2.125 = 0.000 0.000 + x = -3.281101187 + -2.125 x = -3.281101187 + -2.125 Combine like terms: -3.281101187 + -2.125 = -5.406101187 x = -5.406101187 Simplifying x = -5.406101187Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.156101187, -5.406101187}
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