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Simplifying 5[(x + -3)(x + -3)] = 30 Reorder the terms: 5[(-3 + x)(x + -3)] = 30 Reorder the terms: 5[(-3 + x)(-3 + x)] = 30 Multiply (-3 + x) * (-3 + x) 5[(-3(-3 + x) + x(-3 + x))] = 30 5[((-3 * -3 + x * -3) + x(-3 + x))] = 30 5[((9 + -3x) + x(-3 + x))] = 30 5[(9 + -3x + (-3 * x + x * x))] = 30 5[(9 + -3x + (-3x + x2))] = 30 Combine like terms: -3x + -3x = -6x 5[(9 + -6x + x2)] = 30 [9 * 5 + -6x * 5 + x2 * 5] = 30 [45 + -30x + 5x2] = 30 Solving 45 + -30x + 5x2 = 30 Solving for variable 'x'. Reorder the terms: 45 + -30 + -30x + 5x2 = 30 + -30 Combine like terms: 45 + -30 = 15 15 + -30x + 5x2 = 30 + -30 Combine like terms: 30 + -30 = 0 15 + -30x + 5x2 = 0 Factor out the Greatest Common Factor (GCF), '5'. 5(3 + -6x + x2) = 0 Ignore the factor 5.Subproblem 1
Set the factor '(3 + -6x + x2)' equal to zero and attempt to solve: Simplifying 3 + -6x + x2 = 0 Solving 3 + -6x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '-3' to each side of the equation. 3 + -6x + -3 + x2 = 0 + -3 Reorder the terms: 3 + -3 + -6x + x2 = 0 + -3 Combine like terms: 3 + -3 = 0 0 + -6x + x2 = 0 + -3 -6x + x2 = 0 + -3 Combine like terms: 0 + -3 = -3 -6x + x2 = -3 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 = -3 + 9 Reorder the terms: 9 + -6x + x2 = -3 + 9 Combine like terms: -3 + 9 = 6 9 + -6x + x2 = 6 Factor a perfect square on the left side: (x + -3)(x + -3) = 6 Calculate the square root of the right side: 2.449489743 Break this problem into two subproblems by setting (x + -3) equal to 2.449489743 and -2.449489743.Subproblem 1
x + -3 = 2.449489743 Simplifying x + -3 = 2.449489743 Reorder the terms: -3 + x = 2.449489743 Solving -3 + x = 2.449489743 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 = 2.449489743 + 3 Combine like terms: -3 + 3 = 0 0 + x = 2.449489743 + 3 x = 2.449489743 + 3 Combine like terms: 2.449489743 + 3 = 5.449489743 x = 5.449489743 Simplifying x = 5.449489743Subproblem 2
x + -3 = -2.449489743 Simplifying x + -3 = -2.449489743 Reorder the terms: -3 + x = -2.449489743 Solving -3 + x = -2.449489743 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 = -2.449489743 + 3 Combine like terms: -3 + 3 = 0 0 + x = -2.449489743 + 3 x = -2.449489743 + 3 Combine like terms: -2.449489743 + 3 = 0.550510257 x = 0.550510257 Simplifying x = 0.550510257Solution
The solution to the problem is based on the solutions from the subproblems. x = {5.449489743, 0.550510257}Solution
x = {5.449489743, 0.550510257}
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