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Simplifying (x + 4)(x + -7) = 70 Reorder the terms: (4 + x)(x + -7) = 70 Reorder the terms: (4 + x)(-7 + x) = 70 Multiply (4 + x) * (-7 + x) (4(-7 + x) + x(-7 + x)) = 70 ((-7 * 4 + x * 4) + x(-7 + x)) = 70 ((-28 + 4x) + x(-7 + x)) = 70 (-28 + 4x + (-7 * x + x * x)) = 70 (-28 + 4x + (-7x + x2)) = 70 Combine like terms: 4x + -7x = -3x (-28 + -3x + x2) = 70 Solving -28 + -3x + x2 = 70 Solving for variable 'x'. Reorder the terms: -28 + -70 + -3x + x2 = 70 + -70 Combine like terms: -28 + -70 = -98 -98 + -3x + x2 = 70 + -70 Combine like terms: 70 + -70 = 0 -98 + -3x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '98' to each side of the equation. -98 + -3x + 98 + x2 = 0 + 98 Reorder the terms: -98 + 98 + -3x + x2 = 0 + 98 Combine like terms: -98 + 98 = 0 0 + -3x + x2 = 0 + 98 -3x + x2 = 0 + 98 Combine like terms: 0 + 98 = 98 -3x + x2 = 98 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 = 98 + 2.25 Reorder the terms: 2.25 + -3x + x2 = 98 + 2.25 Combine like terms: 98 + 2.25 = 100.25 2.25 + -3x + x2 = 100.25 Factor a perfect square on the left side: (x + -1.5)(x + -1.5) = 100.25 Calculate the square root of the right side: 10.012492197 Break this problem into two subproblems by setting (x + -1.5) equal to 10.012492197 and -10.012492197.Subproblem 1
x + -1.5 = 10.012492197 Simplifying x + -1.5 = 10.012492197 Reorder the terms: -1.5 + x = 10.012492197 Solving -1.5 + x = 10.012492197 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 = 10.012492197 + 1.5 Combine like terms: -1.5 + 1.5 = 0.0 0.0 + x = 10.012492197 + 1.5 x = 10.012492197 + 1.5 Combine like terms: 10.012492197 + 1.5 = 11.512492197 x = 11.512492197 Simplifying x = 11.512492197Subproblem 2
x + -1.5 = -10.012492197 Simplifying x + -1.5 = -10.012492197 Reorder the terms: -1.5 + x = -10.012492197 Solving -1.5 + x = -10.012492197 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 = -10.012492197 + 1.5 Combine like terms: -1.5 + 1.5 = 0.0 0.0 + x = -10.012492197 + 1.5 x = -10.012492197 + 1.5 Combine like terms: -10.012492197 + 1.5 = -8.512492197 x = -8.512492197 Simplifying x = -8.512492197Solution
The solution to the problem is based on the solutions from the subproblems. x = {11.512492197, -8.512492197}
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