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Simplifying 84x2 + -1176x + -3864 = 0 Reorder the terms: -3864 + -1176x + 84x2 = 0 Solving -3864 + -1176x + 84x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '84'. 84(-46 + -14x + x2) = 0 Ignore the factor 84.Subproblem 1
Set the factor '(-46 + -14x + x2)' equal to zero and attempt to solve: Simplifying -46 + -14x + x2 = 0 Solving -46 + -14x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '46' to each side of the equation. -46 + -14x + 46 + x2 = 0 + 46 Reorder the terms: -46 + 46 + -14x + x2 = 0 + 46 Combine like terms: -46 + 46 = 0 0 + -14x + x2 = 0 + 46 -14x + x2 = 0 + 46 Combine like terms: 0 + 46 = 46 -14x + x2 = 46 The x term is -14x. Take half its coefficient (-7). Square it (49) and add it to both sides. Add '49' to each side of the equation. -14x + 49 + x2 = 46 + 49 Reorder the terms: 49 + -14x + x2 = 46 + 49 Combine like terms: 46 + 49 = 95 49 + -14x + x2 = 95 Factor a perfect square on the left side: (x + -7)(x + -7) = 95 Calculate the square root of the right side: 9.746794345 Break this problem into two subproblems by setting (x + -7) equal to 9.746794345 and -9.746794345.Subproblem 1
x + -7 = 9.746794345 Simplifying x + -7 = 9.746794345 Reorder the terms: -7 + x = 9.746794345 Solving -7 + x = 9.746794345 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '7' to each side of the equation. -7 + 7 + x = 9.746794345 + 7 Combine like terms: -7 + 7 = 0 0 + x = 9.746794345 + 7 x = 9.746794345 + 7 Combine like terms: 9.746794345 + 7 = 16.746794345 x = 16.746794345 Simplifying x = 16.746794345Subproblem 2
x + -7 = -9.746794345 Simplifying x + -7 = -9.746794345 Reorder the terms: -7 + x = -9.746794345 Solving -7 + x = -9.746794345 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '7' to each side of the equation. -7 + 7 + x = -9.746794345 + 7 Combine like terms: -7 + 7 = 0 0 + x = -9.746794345 + 7 x = -9.746794345 + 7 Combine like terms: -9.746794345 + 7 = -2.746794345 x = -2.746794345 Simplifying x = -2.746794345Solution
The solution to the problem is based on the solutions from the subproblems. x = {16.746794345, -2.746794345}Solution
x = {16.746794345, -2.746794345}
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