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Simplifying 2[(x + -3)(x + -3)] = 38 Reorder the terms: 2[(-3 + x)(x + -3)] = 38 Reorder the terms: 2[(-3 + x)(-3 + x)] = 38 Multiply (-3 + x) * (-3 + x) 2[(-3(-3 + x) + x(-3 + x))] = 38 2[((-3 * -3 + x * -3) + x(-3 + x))] = 38 2[((9 + -3x) + x(-3 + x))] = 38 2[(9 + -3x + (-3 * x + x * x))] = 38 2[(9 + -3x + (-3x + x2))] = 38 Combine like terms: -3x + -3x = -6x 2[(9 + -6x + x2)] = 38 [9 * 2 + -6x * 2 + x2 * 2] = 38 [18 + -12x + 2x2] = 38 Solving 18 + -12x + 2x2 = 38 Solving for variable 'x'. Reorder the terms: 18 + -38 + -12x + 2x2 = 38 + -38 Combine like terms: 18 + -38 = -20 -20 + -12x + 2x2 = 38 + -38 Combine like terms: 38 + -38 = 0 -20 + -12x + 2x2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(-10 + -6x + x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-10 + -6x + x2)' equal to zero and attempt to solve: Simplifying -10 + -6x + x2 = 0 Solving -10 + -6x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '10' to each side of the equation. -10 + -6x + 10 + x2 = 0 + 10 Reorder the terms: -10 + 10 + -6x + x2 = 0 + 10 Combine like terms: -10 + 10 = 0 0 + -6x + x2 = 0 + 10 -6x + x2 = 0 + 10 Combine like terms: 0 + 10 = 10 -6x + x2 = 10 The x term is -6x. Take half its coefficient (-3). Square it (9) and add it to both sides. Add '9' to each side of the equation. -6x + 9 + x2 = 10 + 9 Reorder the terms: 9 + -6x + x2 = 10 + 9 Combine like terms: 10 + 9 = 19 9 + -6x + x2 = 19 Factor a perfect square on the left side: (x + -3)(x + -3) = 19 Calculate the square root of the right side: 4.358898944 Break this problem into two subproblems by setting (x + -3) equal to 4.358898944 and -4.358898944.Subproblem 1
x + -3 = 4.358898944 Simplifying x + -3 = 4.358898944 Reorder the terms: -3 + x = 4.358898944 Solving -3 + x = 4.358898944 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '3' to each side of the equation. -3 + 3 + x = 4.358898944 + 3 Combine like terms: -3 + 3 = 0 0 + x = 4.358898944 + 3 x = 4.358898944 + 3 Combine like terms: 4.358898944 + 3 = 7.358898944 x = 7.358898944 Simplifying x = 7.358898944Subproblem 2
x + -3 = -4.358898944 Simplifying x + -3 = -4.358898944 Reorder the terms: -3 + x = -4.358898944 Solving -3 + x = -4.358898944 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '3' to each side of the equation. -3 + 3 + x = -4.358898944 + 3 Combine like terms: -3 + 3 = 0 0 + x = -4.358898944 + 3 x = -4.358898944 + 3 Combine like terms: -4.358898944 + 3 = -1.358898944 x = -1.358898944 Simplifying x = -1.358898944Solution
The solution to the problem is based on the solutions from the subproblems. x = {7.358898944, -1.358898944}Solution
x = {7.358898944, -1.358898944}
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