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Simplifying 2(x + 7)(x + -3) = 90 Reorder the terms: 2(7 + x)(x + -3) = 90 Reorder the terms: 2(7 + x)(-3 + x) = 90 Multiply (7 + x) * (-3 + x) 2(7(-3 + x) + x(-3 + x)) = 90 2((-3 * 7 + x * 7) + x(-3 + x)) = 90 2((-21 + 7x) + x(-3 + x)) = 90 2(-21 + 7x + (-3 * x + x * x)) = 90 2(-21 + 7x + (-3x + x2)) = 90 Combine like terms: 7x + -3x = 4x 2(-21 + 4x + x2) = 90 (-21 * 2 + 4x * 2 + x2 * 2) = 90 (-42 + 8x + 2x2) = 90 Solving -42 + 8x + 2x2 = 90 Solving for variable 'x'. Reorder the terms: -42 + -90 + 8x + 2x2 = 90 + -90 Combine like terms: -42 + -90 = -132 -132 + 8x + 2x2 = 90 + -90 Combine like terms: 90 + -90 = 0 -132 + 8x + 2x2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(-66 + 4x + x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-66 + 4x + x2)' equal to zero and attempt to solve: Simplifying -66 + 4x + x2 = 0 Solving -66 + 4x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '66' to each side of the equation. -66 + 4x + 66 + x2 = 0 + 66 Reorder the terms: -66 + 66 + 4x + x2 = 0 + 66 Combine like terms: -66 + 66 = 0 0 + 4x + x2 = 0 + 66 4x + x2 = 0 + 66 Combine like terms: 0 + 66 = 66 4x + x2 = 66 The x term is 4x. Take half its coefficient (2). Square it (4) and add it to both sides. Add '4' to each side of the equation. 4x + 4 + x2 = 66 + 4 Reorder the terms: 4 + 4x + x2 = 66 + 4 Combine like terms: 66 + 4 = 70 4 + 4x + x2 = 70 Factor a perfect square on the left side: (x + 2)(x + 2) = 70 Calculate the square root of the right side: 8.366600265 Break this problem into two subproblems by setting (x + 2) equal to 8.366600265 and -8.366600265.Subproblem 1
x + 2 = 8.366600265 Simplifying x + 2 = 8.366600265 Reorder the terms: 2 + x = 8.366600265 Solving 2 + x = 8.366600265 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + x = 8.366600265 + -2 Combine like terms: 2 + -2 = 0 0 + x = 8.366600265 + -2 x = 8.366600265 + -2 Combine like terms: 8.366600265 + -2 = 6.366600265 x = 6.366600265 Simplifying x = 6.366600265Subproblem 2
x + 2 = -8.366600265 Simplifying x + 2 = -8.366600265 Reorder the terms: 2 + x = -8.366600265 Solving 2 + x = -8.366600265 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + x = -8.366600265 + -2 Combine like terms: 2 + -2 = 0 0 + x = -8.366600265 + -2 x = -8.366600265 + -2 Combine like terms: -8.366600265 + -2 = -10.366600265 x = -10.366600265 Simplifying x = -10.366600265Solution
The solution to the problem is based on the solutions from the subproblems. x = {6.366600265, -10.366600265}Solution
x = {6.366600265, -10.366600265}
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