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Simplifying 5x2 + -70x + -245 = 320 Reorder the terms: -245 + -70x + 5x2 = 320 Solving -245 + -70x + 5x2 = 320 Solving for variable 'x'. Reorder the terms: -245 + -320 + -70x + 5x2 = 320 + -320 Combine like terms: -245 + -320 = -565 -565 + -70x + 5x2 = 320 + -320 Combine like terms: 320 + -320 = 0 -565 + -70x + 5x2 = 0 Factor out the Greatest Common Factor (GCF), '5'. 5(-113 + -14x + x2) = 0 Ignore the factor 5.Subproblem 1
Set the factor '(-113 + -14x + x2)' equal to zero and attempt to solve: Simplifying -113 + -14x + x2 = 0 Solving -113 + -14x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '113' to each side of the equation. -113 + -14x + 113 + x2 = 0 + 113 Reorder the terms: -113 + 113 + -14x + x2 = 0 + 113 Combine like terms: -113 + 113 = 0 0 + -14x + x2 = 0 + 113 -14x + x2 = 0 + 113 Combine like terms: 0 + 113 = 113 -14x + x2 = 113 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 = 113 + 49 Reorder the terms: 49 + -14x + x2 = 113 + 49 Combine like terms: 113 + 49 = 162 49 + -14x + x2 = 162 Factor a perfect square on the left side: (x + -7)(x + -7) = 162 Calculate the square root of the right side: 12.727922061 Break this problem into two subproblems by setting (x + -7) equal to 12.727922061 and -12.727922061.Subproblem 1
x + -7 = 12.727922061 Simplifying x + -7 = 12.727922061 Reorder the terms: -7 + x = 12.727922061 Solving -7 + x = 12.727922061 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 = 12.727922061 + 7 Combine like terms: -7 + 7 = 0 0 + x = 12.727922061 + 7 x = 12.727922061 + 7 Combine like terms: 12.727922061 + 7 = 19.727922061 x = 19.727922061 Simplifying x = 19.727922061Subproblem 2
x + -7 = -12.727922061 Simplifying x + -7 = -12.727922061 Reorder the terms: -7 + x = -12.727922061 Solving -7 + x = -12.727922061 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 = -12.727922061 + 7 Combine like terms: -7 + 7 = 0 0 + x = -12.727922061 + 7 x = -12.727922061 + 7 Combine like terms: -12.727922061 + 7 = -5.727922061 x = -5.727922061 Simplifying x = -5.727922061Solution
The solution to the problem is based on the solutions from the subproblems. x = {19.727922061, -5.727922061}Solution
x = {19.727922061, -5.727922061}
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