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Simplifying -5x2 + 30x + 10 = 0 Reorder the terms: 10 + 30x + -5x2 = 0 Solving 10 + 30x + -5x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '5'. 5(2 + 6x + -1x2) = 0 Ignore the factor 5.Subproblem 1
Set the factor '(2 + 6x + -1x2)' equal to zero and attempt to solve: Simplifying 2 + 6x + -1x2 = 0 Solving 2 + 6x + -1x2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -2 + -6x + x2 = 0 Move the constant term to the right: Add '2' to each side of the equation. -2 + -6x + 2 + x2 = 0 + 2 Reorder the terms: -2 + 2 + -6x + x2 = 0 + 2 Combine like terms: -2 + 2 = 0 0 + -6x + x2 = 0 + 2 -6x + x2 = 0 + 2 Combine like terms: 0 + 2 = 2 -6x + x2 = 2 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 = 2 + 9 Reorder the terms: 9 + -6x + x2 = 2 + 9 Combine like terms: 2 + 9 = 11 9 + -6x + x2 = 11 Factor a perfect square on the left side: (x + -3)(x + -3) = 11 Calculate the square root of the right side: 3.31662479 Break this problem into two subproblems by setting (x + -3) equal to 3.31662479 and -3.31662479.Subproblem 1
x + -3 = 3.31662479 Simplifying x + -3 = 3.31662479 Reorder the terms: -3 + x = 3.31662479 Solving -3 + x = 3.31662479 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 = 3.31662479 + 3 Combine like terms: -3 + 3 = 0 0 + x = 3.31662479 + 3 x = 3.31662479 + 3 Combine like terms: 3.31662479 + 3 = 6.31662479 x = 6.31662479 Simplifying x = 6.31662479Subproblem 2
x + -3 = -3.31662479 Simplifying x + -3 = -3.31662479 Reorder the terms: -3 + x = -3.31662479 Solving -3 + x = -3.31662479 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 = -3.31662479 + 3 Combine like terms: -3 + 3 = 0 0 + x = -3.31662479 + 3 x = -3.31662479 + 3 Combine like terms: -3.31662479 + 3 = -0.31662479 x = -0.31662479 Simplifying x = -0.31662479Solution
The solution to the problem is based on the solutions from the subproblems. x = {6.31662479, -0.31662479}Solution
x = {6.31662479, -0.31662479}
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