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Simplifying 3x2 + 51x + 45 = 0 Reorder the terms: 45 + 51x + 3x2 = 0 Solving 45 + 51x + 3x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '3'. 3(15 + 17x + x2) = 0 Ignore the factor 3.Subproblem 1
Set the factor '(15 + 17x + x2)' equal to zero and attempt to solve: Simplifying 15 + 17x + x2 = 0 Solving 15 + 17x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '-15' to each side of the equation. 15 + 17x + -15 + x2 = 0 + -15 Reorder the terms: 15 + -15 + 17x + x2 = 0 + -15 Combine like terms: 15 + -15 = 0 0 + 17x + x2 = 0 + -15 17x + x2 = 0 + -15 Combine like terms: 0 + -15 = -15 17x + x2 = -15 The x term is 17x. Take half its coefficient (8.5). Square it (72.25) and add it to both sides. Add '72.25' to each side of the equation. 17x + 72.25 + x2 = -15 + 72.25 Reorder the terms: 72.25 + 17x + x2 = -15 + 72.25 Combine like terms: -15 + 72.25 = 57.25 72.25 + 17x + x2 = 57.25 Factor a perfect square on the left side: (x + 8.5)(x + 8.5) = 57.25 Calculate the square root of the right side: 7.566372975 Break this problem into two subproblems by setting (x + 8.5) equal to 7.566372975 and -7.566372975.Subproblem 1
x + 8.5 = 7.566372975 Simplifying x + 8.5 = 7.566372975 Reorder the terms: 8.5 + x = 7.566372975 Solving 8.5 + x = 7.566372975 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-8.5' to each side of the equation. 8.5 + -8.5 + x = 7.566372975 + -8.5 Combine like terms: 8.5 + -8.5 = 0.0 0.0 + x = 7.566372975 + -8.5 x = 7.566372975 + -8.5 Combine like terms: 7.566372975 + -8.5 = -0.933627025 x = -0.933627025 Simplifying x = -0.933627025Subproblem 2
x + 8.5 = -7.566372975 Simplifying x + 8.5 = -7.566372975 Reorder the terms: 8.5 + x = -7.566372975 Solving 8.5 + x = -7.566372975 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-8.5' to each side of the equation. 8.5 + -8.5 + x = -7.566372975 + -8.5 Combine like terms: 8.5 + -8.5 = 0.0 0.0 + x = -7.566372975 + -8.5 x = -7.566372975 + -8.5 Combine like terms: -7.566372975 + -8.5 = -16.066372975 x = -16.066372975 Simplifying x = -16.066372975Solution
The solution to the problem is based on the solutions from the subproblems. x = {-0.933627025, -16.066372975}Solution
x = {-0.933627025, -16.066372975}
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