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Simplifying -5x2 + -30x + -3 = 0 Reorder the terms: -3 + -30x + -5x2 = 0 Solving -3 + -30x + -5x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '-1'. -1(3 + 30x + 5x2) = 0 Ignore the factor -1.Subproblem 1
Set the factor '(3 + 30x + 5x2)' equal to zero and attempt to solve: Simplifying 3 + 30x + 5x2 = 0 Solving 3 + 30x + 5x2 = 0 Begin completing the square. Divide all terms by 5 the coefficient of the squared term: Divide each side by '5'. 0.6 + 6x + x2 = 0 Move the constant term to the right: Add '-0.6' to each side of the equation. 0.6 + 6x + -0.6 + x2 = 0 + -0.6 Reorder the terms: 0.6 + -0.6 + 6x + x2 = 0 + -0.6 Combine like terms: 0.6 + -0.6 = 0.0 0.0 + 6x + x2 = 0 + -0.6 6x + x2 = 0 + -0.6 Combine like terms: 0 + -0.6 = -0.6 6x + x2 = -0.6 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 = -0.6 + 9 Reorder the terms: 9 + 6x + x2 = -0.6 + 9 Combine like terms: -0.6 + 9 = 8.4 9 + 6x + x2 = 8.4 Factor a perfect square on the left side: (x + 3)(x + 3) = 8.4 Calculate the square root of the right side: 2.898275349 Break this problem into two subproblems by setting (x + 3) equal to 2.898275349 and -2.898275349.Subproblem 1
x + 3 = 2.898275349 Simplifying x + 3 = 2.898275349 Reorder the terms: 3 + x = 2.898275349 Solving 3 + x = 2.898275349 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 = 2.898275349 + -3 Combine like terms: 3 + -3 = 0 0 + x = 2.898275349 + -3 x = 2.898275349 + -3 Combine like terms: 2.898275349 + -3 = -0.101724651 x = -0.101724651 Simplifying x = -0.101724651Subproblem 2
x + 3 = -2.898275349 Simplifying x + 3 = -2.898275349 Reorder the terms: 3 + x = -2.898275349 Solving 3 + x = -2.898275349 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 = -2.898275349 + -3 Combine like terms: 3 + -3 = 0 0 + x = -2.898275349 + -3 x = -2.898275349 + -3 Combine like terms: -2.898275349 + -3 = -5.898275349 x = -5.898275349 Simplifying x = -5.898275349Solution
The solution to the problem is based on the solutions from the subproblems. x = {-0.101724651, -5.898275349}Solution
x = {-0.101724651, -5.898275349}
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