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Simplifying 0 = 3x2 + -42x + -150 Reorder the terms: 0 = -150 + -42x + 3x2 Solving 0 = -150 + -42x + 3x2 Solving for variable 'x'. Combine like terms: 0 + 150 = 150 150 + 42x + -3x2 = -150 + -42x + 3x2 + 150 + 42x + -3x2 Reorder the terms: 150 + 42x + -3x2 = -150 + 150 + -42x + 42x + 3x2 + -3x2 Combine like terms: -150 + 150 = 0 150 + 42x + -3x2 = 0 + -42x + 42x + 3x2 + -3x2 150 + 42x + -3x2 = -42x + 42x + 3x2 + -3x2 Combine like terms: -42x + 42x = 0 150 + 42x + -3x2 = 0 + 3x2 + -3x2 150 + 42x + -3x2 = 3x2 + -3x2 Combine like terms: 3x2 + -3x2 = 0 150 + 42x + -3x2 = 0 Factor out the Greatest Common Factor (GCF), '3'. 3(50 + 14x + -1x2) = 0 Ignore the factor 3.Subproblem 1
Set the factor '(50 + 14x + -1x2)' equal to zero and attempt to solve: Simplifying 50 + 14x + -1x2 = 0 Solving 50 + 14x + -1x2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -50 + -14x + x2 = 0 Move the constant term to the right: Add '50' to each side of the equation. -50 + -14x + 50 + x2 = 0 + 50 Reorder the terms: -50 + 50 + -14x + x2 = 0 + 50 Combine like terms: -50 + 50 = 0 0 + -14x + x2 = 0 + 50 -14x + x2 = 0 + 50 Combine like terms: 0 + 50 = 50 -14x + x2 = 50 The x term is -14x. Take half its coefficient (-7). Square it (49) and add it to both sides. Add '49' to each side of the equation. -14x + 49 + x2 = 50 + 49 Reorder the terms: 49 + -14x + x2 = 50 + 49 Combine like terms: 50 + 49 = 99 49 + -14x + x2 = 99 Factor a perfect square on the left side: (x + -7)(x + -7) = 99 Calculate the square root of the right side: 9.949874371 Break this problem into two subproblems by setting (x + -7) equal to 9.949874371 and -9.949874371.Subproblem 1
x + -7 = 9.949874371 Simplifying x + -7 = 9.949874371 Reorder the terms: -7 + x = 9.949874371 Solving -7 + x = 9.949874371 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '7' to each side of the equation. -7 + 7 + x = 9.949874371 + 7 Combine like terms: -7 + 7 = 0 0 + x = 9.949874371 + 7 x = 9.949874371 + 7 Combine like terms: 9.949874371 + 7 = 16.949874371 x = 16.949874371 Simplifying x = 16.949874371Subproblem 2
x + -7 = -9.949874371 Simplifying x + -7 = -9.949874371 Reorder the terms: -7 + x = -9.949874371 Solving -7 + x = -9.949874371 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '7' to each side of the equation. -7 + 7 + x = -9.949874371 + 7 Combine like terms: -7 + 7 = 0 0 + x = -9.949874371 + 7 x = -9.949874371 + 7 Combine like terms: -9.949874371 + 7 = -2.949874371 x = -2.949874371 Simplifying x = -2.949874371Solution
The solution to the problem is based on the solutions from the subproblems. x = {16.949874371, -2.949874371}Solution
x = {16.949874371, -2.949874371}
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