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Simplifying 3(x2 + 6x + -756) = 0 Reorder the terms: 3(-756 + 6x + x2) = 0 (-756 * 3 + 6x * 3 + x2 * 3) = 0 (-2268 + 18x + 3x2) = 0 Solving -2268 + 18x + 3x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '3'. 3(-756 + 6x + x2) = 0 Ignore the factor 3.Subproblem 1
Set the factor '(-756 + 6x + x2)' equal to zero and attempt to solve: Simplifying -756 + 6x + x2 = 0 Solving -756 + 6x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '756' to each side of the equation. -756 + 6x + 756 + x2 = 0 + 756 Reorder the terms: -756 + 756 + 6x + x2 = 0 + 756 Combine like terms: -756 + 756 = 0 0 + 6x + x2 = 0 + 756 6x + x2 = 0 + 756 Combine like terms: 0 + 756 = 756 6x + x2 = 756 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 = 756 + 9 Reorder the terms: 9 + 6x + x2 = 756 + 9 Combine like terms: 756 + 9 = 765 9 + 6x + x2 = 765 Factor a perfect square on the left side: (x + 3)(x + 3) = 765 Calculate the square root of the right side: 27.658633372 Break this problem into two subproblems by setting (x + 3) equal to 27.658633372 and -27.658633372.Subproblem 1
x + 3 = 27.658633372 Simplifying x + 3 = 27.658633372 Reorder the terms: 3 + x = 27.658633372 Solving 3 + x = 27.658633372 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 = 27.658633372 + -3 Combine like terms: 3 + -3 = 0 0 + x = 27.658633372 + -3 x = 27.658633372 + -3 Combine like terms: 27.658633372 + -3 = 24.658633372 x = 24.658633372 Simplifying x = 24.658633372Subproblem 2
x + 3 = -27.658633372 Simplifying x + 3 = -27.658633372 Reorder the terms: 3 + x = -27.658633372 Solving 3 + x = -27.658633372 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 = -27.658633372 + -3 Combine like terms: 3 + -3 = 0 0 + x = -27.658633372 + -3 x = -27.658633372 + -3 Combine like terms: -27.658633372 + -3 = -30.658633372 x = -30.658633372 Simplifying x = -30.658633372Solution
The solution to the problem is based on the solutions from the subproblems. x = {24.658633372, -30.658633372}Solution
x = {24.658633372, -30.658633372}
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