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Simplifying 5x2 + 30x = 75 Reorder the terms: 30x + 5x2 = 75 Solving 30x + 5x2 = 75 Solving for variable 'x'. Reorder the terms: -75 + 30x + 5x2 = 75 + -75 Combine like terms: 75 + -75 = 0 -75 + 30x + 5x2 = 0 Factor out the Greatest Common Factor (GCF), '5'. 5(-15 + 6x + x2) = 0 Ignore the factor 5.Subproblem 1
Set the factor '(-15 + 6x + x2)' equal to zero and attempt to solve: Simplifying -15 + 6x + x2 = 0 Solving -15 + 6x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '15' to each side of the equation. -15 + 6x + 15 + x2 = 0 + 15 Reorder the terms: -15 + 15 + 6x + x2 = 0 + 15 Combine like terms: -15 + 15 = 0 0 + 6x + x2 = 0 + 15 6x + x2 = 0 + 15 Combine like terms: 0 + 15 = 15 6x + x2 = 15 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 = 15 + 9 Reorder the terms: 9 + 6x + x2 = 15 + 9 Combine like terms: 15 + 9 = 24 9 + 6x + x2 = 24 Factor a perfect square on the left side: (x + 3)(x + 3) = 24 Calculate the square root of the right side: 4.898979486 Break this problem into two subproblems by setting (x + 3) equal to 4.898979486 and -4.898979486.Subproblem 1
x + 3 = 4.898979486 Simplifying x + 3 = 4.898979486 Reorder the terms: 3 + x = 4.898979486 Solving 3 + x = 4.898979486 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 = 4.898979486 + -3 Combine like terms: 3 + -3 = 0 0 + x = 4.898979486 + -3 x = 4.898979486 + -3 Combine like terms: 4.898979486 + -3 = 1.898979486 x = 1.898979486 Simplifying x = 1.898979486Subproblem 2
x + 3 = -4.898979486 Simplifying x + 3 = -4.898979486 Reorder the terms: 3 + x = -4.898979486 Solving 3 + x = -4.898979486 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 = -4.898979486 + -3 Combine like terms: 3 + -3 = 0 0 + x = -4.898979486 + -3 x = -4.898979486 + -3 Combine like terms: -4.898979486 + -3 = -7.898979486 x = -7.898979486 Simplifying x = -7.898979486Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.898979486, -7.898979486}Solution
x = {1.898979486, -7.898979486}
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