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Simplifying 4(x2) = (x + 10)(x + 2) Reorder the terms: 4x2 = (10 + x)(x + 2) Reorder the terms: 4x2 = (10 + x)(2 + x) Multiply (10 + x) * (2 + x) 4x2 = (10(2 + x) + x(2 + x)) 4x2 = ((2 * 10 + x * 10) + x(2 + x)) 4x2 = ((20 + 10x) + x(2 + x)) 4x2 = (20 + 10x + (2 * x + x * x)) 4x2 = (20 + 10x + (2x + x2)) Combine like terms: 10x + 2x = 12x 4x2 = (20 + 12x + x2) Solving 4x2 = 20 + 12x + x2 Solving for variable 'x'. Reorder the terms: -20 + -12x + 4x2 + -1x2 = 20 + 12x + x2 + -20 + -12x + -1x2 Combine like terms: 4x2 + -1x2 = 3x2 -20 + -12x + 3x2 = 20 + 12x + x2 + -20 + -12x + -1x2 Reorder the terms: -20 + -12x + 3x2 = 20 + -20 + 12x + -12x + x2 + -1x2 Combine like terms: 20 + -20 = 0 -20 + -12x + 3x2 = 0 + 12x + -12x + x2 + -1x2 -20 + -12x + 3x2 = 12x + -12x + x2 + -1x2 Combine like terms: 12x + -12x = 0 -20 + -12x + 3x2 = 0 + x2 + -1x2 -20 + -12x + 3x2 = x2 + -1x2 Combine like terms: x2 + -1x2 = 0 -20 + -12x + 3x2 = 0 Begin completing the square. Divide all terms by 3 the coefficient of the squared term: Divide each side by '3'. -6.666666667 + -4x + x2 = 0 Move the constant term to the right: Add '6.666666667' to each side of the equation. -6.666666667 + -4x + 6.666666667 + x2 = 0 + 6.666666667 Reorder the terms: -6.666666667 + 6.666666667 + -4x + x2 = 0 + 6.666666667 Combine like terms: -6.666666667 + 6.666666667 = 0.000000000 0.000000000 + -4x + x2 = 0 + 6.666666667 -4x + x2 = 0 + 6.666666667 Combine like terms: 0 + 6.666666667 = 6.666666667 -4x + x2 = 6.666666667 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 = 6.666666667 + 4 Reorder the terms: 4 + -4x + x2 = 6.666666667 + 4 Combine like terms: 6.666666667 + 4 = 10.666666667 4 + -4x + x2 = 10.666666667 Factor a perfect square on the left side: (x + -2)(x + -2) = 10.666666667 Calculate the square root of the right side: 3.265986324 Break this problem into two subproblems by setting (x + -2) equal to 3.265986324 and -3.265986324.Subproblem 1
x + -2 = 3.265986324 Simplifying x + -2 = 3.265986324 Reorder the terms: -2 + x = 3.265986324 Solving -2 + x = 3.265986324 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 = 3.265986324 + 2 Combine like terms: -2 + 2 = 0 0 + x = 3.265986324 + 2 x = 3.265986324 + 2 Combine like terms: 3.265986324 + 2 = 5.265986324 x = 5.265986324 Simplifying x = 5.265986324Subproblem 2
x + -2 = -3.265986324 Simplifying x + -2 = -3.265986324 Reorder the terms: -2 + x = -3.265986324 Solving -2 + x = -3.265986324 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 = -3.265986324 + 2 Combine like terms: -2 + 2 = 0 0 + x = -3.265986324 + 2 x = -3.265986324 + 2 Combine like terms: -3.265986324 + 2 = -1.265986324 x = -1.265986324 Simplifying x = -1.265986324Solution
The solution to the problem is based on the solutions from the subproblems. x = {5.265986324, -1.265986324}
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