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Simplifying -150x2 + 300x + 10 = 0 Reorder the terms: 10 + 300x + -150x2 = 0 Solving 10 + 300x + -150x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '10'. 10(1 + 30x + -15x2) = 0 Ignore the factor 10.Subproblem 1
Set the factor '(1 + 30x + -15x2)' equal to zero and attempt to solve: Simplifying 1 + 30x + -15x2 = 0 Solving 1 + 30x + -15x2 = 0 Begin completing the square. Divide all terms by -15 the coefficient of the squared term: Divide each side by '-15'. -0.06666666667 + -2x + x2 = 0 Move the constant term to the right: Add '0.06666666667' to each side of the equation. -0.06666666667 + -2x + 0.06666666667 + x2 = 0 + 0.06666666667 Reorder the terms: -0.06666666667 + 0.06666666667 + -2x + x2 = 0 + 0.06666666667 Combine like terms: -0.06666666667 + 0.06666666667 = 0.00000000000 0.00000000000 + -2x + x2 = 0 + 0.06666666667 -2x + x2 = 0 + 0.06666666667 Combine like terms: 0 + 0.06666666667 = 0.06666666667 -2x + x2 = 0.06666666667 The x term is -2x. Take half its coefficient (-1). Square it (1) and add it to both sides. Add '1' to each side of the equation. -2x + 1 + x2 = 0.06666666667 + 1 Reorder the terms: 1 + -2x + x2 = 0.06666666667 + 1 Combine like terms: 0.06666666667 + 1 = 1.06666666667 1 + -2x + x2 = 1.06666666667 Factor a perfect square on the left side: (x + -1)(x + -1) = 1.06666666667 Calculate the square root of the right side: 1.032795559 Break this problem into two subproblems by setting (x + -1) equal to 1.032795559 and -1.032795559.Subproblem 1
x + -1 = 1.032795559 Simplifying x + -1 = 1.032795559 Reorder the terms: -1 + x = 1.032795559 Solving -1 + x = 1.032795559 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1' to each side of the equation. -1 + 1 + x = 1.032795559 + 1 Combine like terms: -1 + 1 = 0 0 + x = 1.032795559 + 1 x = 1.032795559 + 1 Combine like terms: 1.032795559 + 1 = 2.032795559 x = 2.032795559 Simplifying x = 2.032795559Subproblem 2
x + -1 = -1.032795559 Simplifying x + -1 = -1.032795559 Reorder the terms: -1 + x = -1.032795559 Solving -1 + x = -1.032795559 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1' to each side of the equation. -1 + 1 + x = -1.032795559 + 1 Combine like terms: -1 + 1 = 0 0 + x = -1.032795559 + 1 x = -1.032795559 + 1 Combine like terms: -1.032795559 + 1 = -0.032795559 x = -0.032795559 Simplifying x = -0.032795559Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.032795559, -0.032795559}Solution
x = {2.032795559, -0.032795559}
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