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Simplifying 0 = 6x2 + -30x + 18 Reorder the terms: 0 = 18 + -30x + 6x2 Solving 0 = 18 + -30x + 6x2 Solving for variable 'x'. Combine like terms: 0 + -18 = -18 -18 + 30x + -6x2 = 18 + -30x + 6x2 + -18 + 30x + -6x2 Reorder the terms: -18 + 30x + -6x2 = 18 + -18 + -30x + 30x + 6x2 + -6x2 Combine like terms: 18 + -18 = 0 -18 + 30x + -6x2 = 0 + -30x + 30x + 6x2 + -6x2 -18 + 30x + -6x2 = -30x + 30x + 6x2 + -6x2 Combine like terms: -30x + 30x = 0 -18 + 30x + -6x2 = 0 + 6x2 + -6x2 -18 + 30x + -6x2 = 6x2 + -6x2 Combine like terms: 6x2 + -6x2 = 0 -18 + 30x + -6x2 = 0 Factor out the Greatest Common Factor (GCF), '6'. 6(-3 + 5x + -1x2) = 0 Ignore the factor 6.Subproblem 1
Set the factor '(-3 + 5x + -1x2)' equal to zero and attempt to solve: Simplifying -3 + 5x + -1x2 = 0 Solving -3 + 5x + -1x2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. 3 + -5x + x2 = 0 Move the constant term to the right: Add '-3' to each side of the equation. 3 + -5x + -3 + x2 = 0 + -3 Reorder the terms: 3 + -3 + -5x + x2 = 0 + -3 Combine like terms: 3 + -3 = 0 0 + -5x + x2 = 0 + -3 -5x + x2 = 0 + -3 Combine like terms: 0 + -3 = -3 -5x + x2 = -3 The x term is -5x. Take half its coefficient (-2.5). Square it (6.25) and add it to both sides. Add '6.25' to each side of the equation. -5x + 6.25 + x2 = -3 + 6.25 Reorder the terms: 6.25 + -5x + x2 = -3 + 6.25 Combine like terms: -3 + 6.25 = 3.25 6.25 + -5x + x2 = 3.25 Factor a perfect square on the left side: (x + -2.5)(x + -2.5) = 3.25 Calculate the square root of the right side: 1.802775638 Break this problem into two subproblems by setting (x + -2.5) equal to 1.802775638 and -1.802775638.Subproblem 1
x + -2.5 = 1.802775638 Simplifying x + -2.5 = 1.802775638 Reorder the terms: -2.5 + x = 1.802775638 Solving -2.5 + x = 1.802775638 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.5' to each side of the equation. -2.5 + 2.5 + x = 1.802775638 + 2.5 Combine like terms: -2.5 + 2.5 = 0.0 0.0 + x = 1.802775638 + 2.5 x = 1.802775638 + 2.5 Combine like terms: 1.802775638 + 2.5 = 4.302775638 x = 4.302775638 Simplifying x = 4.302775638Subproblem 2
x + -2.5 = -1.802775638 Simplifying x + -2.5 = -1.802775638 Reorder the terms: -2.5 + x = -1.802775638 Solving -2.5 + x = -1.802775638 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.5' to each side of the equation. -2.5 + 2.5 + x = -1.802775638 + 2.5 Combine like terms: -2.5 + 2.5 = 0.0 0.0 + x = -1.802775638 + 2.5 x = -1.802775638 + 2.5 Combine like terms: -1.802775638 + 2.5 = 0.697224362 x = 0.697224362 Simplifying x = 0.697224362Solution
The solution to the problem is based on the solutions from the subproblems. x = {4.302775638, 0.697224362}Solution
x = {4.302775638, 0.697224362}
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