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Simplifying (4x + -7)(x + -5) = 12x + 21 Reorder the terms: (-7 + 4x)(x + -5) = 12x + 21 Reorder the terms: (-7 + 4x)(-5 + x) = 12x + 21 Multiply (-7 + 4x) * (-5 + x) (-7(-5 + x) + 4x * (-5 + x)) = 12x + 21 ((-5 * -7 + x * -7) + 4x * (-5 + x)) = 12x + 21 ((35 + -7x) + 4x * (-5 + x)) = 12x + 21 (35 + -7x + (-5 * 4x + x * 4x)) = 12x + 21 (35 + -7x + (-20x + 4x2)) = 12x + 21 Combine like terms: -7x + -20x = -27x (35 + -27x + 4x2) = 12x + 21 Reorder the terms: 35 + -27x + 4x2 = 21 + 12x Solving 35 + -27x + 4x2 = 21 + 12x Solving for variable 'x'. Reorder the terms: 35 + -21 + -27x + -12x + 4x2 = 21 + 12x + -21 + -12x Combine like terms: 35 + -21 = 14 14 + -27x + -12x + 4x2 = 21 + 12x + -21 + -12x Combine like terms: -27x + -12x = -39x 14 + -39x + 4x2 = 21 + 12x + -21 + -12x Reorder the terms: 14 + -39x + 4x2 = 21 + -21 + 12x + -12x Combine like terms: 21 + -21 = 0 14 + -39x + 4x2 = 0 + 12x + -12x 14 + -39x + 4x2 = 12x + -12x Combine like terms: 12x + -12x = 0 14 + -39x + 4x2 = 0 Begin completing the square. Divide all terms by 4 the coefficient of the squared term: Divide each side by '4'. 3.5 + -9.75x + x2 = 0 Move the constant term to the right: Add '-3.5' to each side of the equation. 3.5 + -9.75x + -3.5 + x2 = 0 + -3.5 Reorder the terms: 3.5 + -3.5 + -9.75x + x2 = 0 + -3.5 Combine like terms: 3.5 + -3.5 = 0.0 0.0 + -9.75x + x2 = 0 + -3.5 -9.75x + x2 = 0 + -3.5 Combine like terms: 0 + -3.5 = -3.5 -9.75x + x2 = -3.5 The x term is -9.75x. Take half its coefficient (-4.875). Square it (23.765625) and add it to both sides. Add '23.765625' to each side of the equation. -9.75x + 23.765625 + x2 = -3.5 + 23.765625 Reorder the terms: 23.765625 + -9.75x + x2 = -3.5 + 23.765625 Combine like terms: -3.5 + 23.765625 = 20.265625 23.765625 + -9.75x + x2 = 20.265625 Factor a perfect square on the left side: (x + -4.875)(x + -4.875) = 20.265625 Calculate the square root of the right side: 4.501735776 Break this problem into two subproblems by setting (x + -4.875) equal to 4.501735776 and -4.501735776.Subproblem 1
x + -4.875 = 4.501735776 Simplifying x + -4.875 = 4.501735776 Reorder the terms: -4.875 + x = 4.501735776 Solving -4.875 + x = 4.501735776 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '4.875' to each side of the equation. -4.875 + 4.875 + x = 4.501735776 + 4.875 Combine like terms: -4.875 + 4.875 = 0.000 0.000 + x = 4.501735776 + 4.875 x = 4.501735776 + 4.875 Combine like terms: 4.501735776 + 4.875 = 9.376735776 x = 9.376735776 Simplifying x = 9.376735776Subproblem 2
x + -4.875 = -4.501735776 Simplifying x + -4.875 = -4.501735776 Reorder the terms: -4.875 + x = -4.501735776 Solving -4.875 + x = -4.501735776 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '4.875' to each side of the equation. -4.875 + 4.875 + x = -4.501735776 + 4.875 Combine like terms: -4.875 + 4.875 = 0.000 0.000 + x = -4.501735776 + 4.875 x = -4.501735776 + 4.875 Combine like terms: -4.501735776 + 4.875 = 0.373264224 x = 0.373264224 Simplifying x = 0.373264224Solution
The solution to the problem is based on the solutions from the subproblems. x = {9.376735776, 0.373264224}
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