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Simplifying 2(x + 7)(x + -3) = 8100 Reorder the terms: 2(7 + x)(x + -3) = 8100 Reorder the terms: 2(7 + x)(-3 + x) = 8100 Multiply (7 + x) * (-3 + x) 2(7(-3 + x) + x(-3 + x)) = 8100 2((-3 * 7 + x * 7) + x(-3 + x)) = 8100 2((-21 + 7x) + x(-3 + x)) = 8100 2(-21 + 7x + (-3 * x + x * x)) = 8100 2(-21 + 7x + (-3x + x2)) = 8100 Combine like terms: 7x + -3x = 4x 2(-21 + 4x + x2) = 8100 (-21 * 2 + 4x * 2 + x2 * 2) = 8100 (-42 + 8x + 2x2) = 8100 Solving -42 + 8x + 2x2 = 8100 Solving for variable 'x'. Reorder the terms: -42 + -8100 + 8x + 2x2 = 8100 + -8100 Combine like terms: -42 + -8100 = -8142 -8142 + 8x + 2x2 = 8100 + -8100 Combine like terms: 8100 + -8100 = 0 -8142 + 8x + 2x2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(-4071 + 4x + x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-4071 + 4x + x2)' equal to zero and attempt to solve: Simplifying -4071 + 4x + x2 = 0 Solving -4071 + 4x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '4071' to each side of the equation. -4071 + 4x + 4071 + x2 = 0 + 4071 Reorder the terms: -4071 + 4071 + 4x + x2 = 0 + 4071 Combine like terms: -4071 + 4071 = 0 0 + 4x + x2 = 0 + 4071 4x + x2 = 0 + 4071 Combine like terms: 0 + 4071 = 4071 4x + x2 = 4071 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 = 4071 + 4 Reorder the terms: 4 + 4x + x2 = 4071 + 4 Combine like terms: 4071 + 4 = 4075 4 + 4x + x2 = 4075 Factor a perfect square on the left side: (x + 2)(x + 2) = 4075 Calculate the square root of the right side: 63.835726674 Break this problem into two subproblems by setting (x + 2) equal to 63.835726674 and -63.835726674.Subproblem 1
x + 2 = 63.835726674 Simplifying x + 2 = 63.835726674 Reorder the terms: 2 + x = 63.835726674 Solving 2 + x = 63.835726674 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 = 63.835726674 + -2 Combine like terms: 2 + -2 = 0 0 + x = 63.835726674 + -2 x = 63.835726674 + -2 Combine like terms: 63.835726674 + -2 = 61.835726674 x = 61.835726674 Simplifying x = 61.835726674Subproblem 2
x + 2 = -63.835726674 Simplifying x + 2 = -63.835726674 Reorder the terms: 2 + x = -63.835726674 Solving 2 + x = -63.835726674 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 = -63.835726674 + -2 Combine like terms: 2 + -2 = 0 0 + x = -63.835726674 + -2 x = -63.835726674 + -2 Combine like terms: -63.835726674 + -2 = -65.835726674 x = -65.835726674 Simplifying x = -65.835726674Solution
The solution to the problem is based on the solutions from the subproblems. x = {61.835726674, -65.835726674}Solution
x = {61.835726674, -65.835726674}
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