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Simplifying 0 = 5x2 + -70x + 75 Reorder the terms: 0 = 75 + -70x + 5x2 Solving 0 = 75 + -70x + 5x2 Solving for variable 'x'. Combine like terms: 0 + -75 = -75 -75 + 70x + -5x2 = 75 + -70x + 5x2 + -75 + 70x + -5x2 Reorder the terms: -75 + 70x + -5x2 = 75 + -75 + -70x + 70x + 5x2 + -5x2 Combine like terms: 75 + -75 = 0 -75 + 70x + -5x2 = 0 + -70x + 70x + 5x2 + -5x2 -75 + 70x + -5x2 = -70x + 70x + 5x2 + -5x2 Combine like terms: -70x + 70x = 0 -75 + 70x + -5x2 = 0 + 5x2 + -5x2 -75 + 70x + -5x2 = 5x2 + -5x2 Combine like terms: 5x2 + -5x2 = 0 -75 + 70x + -5x2 = 0 Factor out the Greatest Common Factor (GCF), '5'. 5(-15 + 14x + -1x2) = 0 Ignore the factor 5.Subproblem 1
Set the factor '(-15 + 14x + -1x2)' equal to zero and attempt to solve: Simplifying -15 + 14x + -1x2 = 0 Solving -15 + 14x + -1x2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. 15 + -14x + x2 = 0 Move the constant term to the right: Add '-15' to each side of the equation. 15 + -14x + -15 + x2 = 0 + -15 Reorder the terms: 15 + -15 + -14x + x2 = 0 + -15 Combine like terms: 15 + -15 = 0 0 + -14x + x2 = 0 + -15 -14x + x2 = 0 + -15 Combine like terms: 0 + -15 = -15 -14x + x2 = -15 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 = -15 + 49 Reorder the terms: 49 + -14x + x2 = -15 + 49 Combine like terms: -15 + 49 = 34 49 + -14x + x2 = 34 Factor a perfect square on the left side: (x + -7)(x + -7) = 34 Calculate the square root of the right side: 5.830951895 Break this problem into two subproblems by setting (x + -7) equal to 5.830951895 and -5.830951895.Subproblem 1
x + -7 = 5.830951895 Simplifying x + -7 = 5.830951895 Reorder the terms: -7 + x = 5.830951895 Solving -7 + x = 5.830951895 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 = 5.830951895 + 7 Combine like terms: -7 + 7 = 0 0 + x = 5.830951895 + 7 x = 5.830951895 + 7 Combine like terms: 5.830951895 + 7 = 12.830951895 x = 12.830951895 Simplifying x = 12.830951895Subproblem 2
x + -7 = -5.830951895 Simplifying x + -7 = -5.830951895 Reorder the terms: -7 + x = -5.830951895 Solving -7 + x = -5.830951895 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 = -5.830951895 + 7 Combine like terms: -7 + 7 = 0 0 + x = -5.830951895 + 7 x = -5.830951895 + 7 Combine like terms: -5.830951895 + 7 = 1.169048105 x = 1.169048105 Simplifying x = 1.169048105Solution
The solution to the problem is based on the solutions from the subproblems. x = {12.830951895, 1.169048105}Solution
x = {12.830951895, 1.169048105}
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