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Simplifying x2 + -210x + 70 = 0 Reorder the terms: 70 + -210x + x2 = 0 Solving 70 + -210x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '-70' to each side of the equation. 70 + -210x + -70 + x2 = 0 + -70 Reorder the terms: 70 + -70 + -210x + x2 = 0 + -70 Combine like terms: 70 + -70 = 0 0 + -210x + x2 = 0 + -70 -210x + x2 = 0 + -70 Combine like terms: 0 + -70 = -70 -210x + x2 = -70 The x term is -210x. Take half its coefficient (-105). Square it (11025) and add it to both sides. Add '11025' to each side of the equation. -210x + 11025 + x2 = -70 + 11025 Reorder the terms: 11025 + -210x + x2 = -70 + 11025 Combine like terms: -70 + 11025 = 10955 11025 + -210x + x2 = 10955 Factor a perfect square on the left side: (x + -105)(x + -105) = 10955 Calculate the square root of the right side: 104.66613588 Break this problem into two subproblems by setting (x + -105) equal to 104.66613588 and -104.66613588.Subproblem 1
x + -105 = 104.66613588 Simplifying x + -105 = 104.66613588 Reorder the terms: -105 + x = 104.66613588 Solving -105 + x = 104.66613588 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '105' to each side of the equation. -105 + 105 + x = 104.66613588 + 105 Combine like terms: -105 + 105 = 0 0 + x = 104.66613588 + 105 x = 104.66613588 + 105 Combine like terms: 104.66613588 + 105 = 209.66613588 x = 209.66613588 Simplifying x = 209.66613588Subproblem 2
x + -105 = -104.66613588 Simplifying x + -105 = -104.66613588 Reorder the terms: -105 + x = -104.66613588 Solving -105 + x = -104.66613588 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '105' to each side of the equation. -105 + 105 + x = -104.66613588 + 105 Combine like terms: -105 + 105 = 0 0 + x = -104.66613588 + 105 x = -104.66613588 + 105 Combine like terms: -104.66613588 + 105 = 0.33386412 x = 0.33386412 Simplifying x = 0.33386412Solution
The solution to the problem is based on the solutions from the subproblems. x = {209.66613588, 0.33386412}
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