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Simplifying (x2) + -1(28x) + -200 = 0 x2 + -1(28x) + -200 = 0 Remove parenthesis around (28x) x2 + -1 * 28x + -200 = 0 Multiply -1 * 28 x2 + -28x + -200 = 0 Reorder the terms: -200 + -28x + x2 = 0 Solving -200 + -28x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '200' to each side of the equation. -200 + -28x + 200 + x2 = 0 + 200 Reorder the terms: -200 + 200 + -28x + x2 = 0 + 200 Combine like terms: -200 + 200 = 0 0 + -28x + x2 = 0 + 200 -28x + x2 = 0 + 200 Combine like terms: 0 + 200 = 200 -28x + x2 = 200 The x term is -28x. Take half its coefficient (-14). Square it (196) and add it to both sides. Add '196' to each side of the equation. -28x + 196 + x2 = 200 + 196 Reorder the terms: 196 + -28x + x2 = 200 + 196 Combine like terms: 200 + 196 = 396 196 + -28x + x2 = 396 Factor a perfect square on the left side: (x + -14)(x + -14) = 396 Calculate the square root of the right side: 19.899748742 Break this problem into two subproblems by setting (x + -14) equal to 19.899748742 and -19.899748742.Subproblem 1
x + -14 = 19.899748742 Simplifying x + -14 = 19.899748742 Reorder the terms: -14 + x = 19.899748742 Solving -14 + x = 19.899748742 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '14' to each side of the equation. -14 + 14 + x = 19.899748742 + 14 Combine like terms: -14 + 14 = 0 0 + x = 19.899748742 + 14 x = 19.899748742 + 14 Combine like terms: 19.899748742 + 14 = 33.899748742 x = 33.899748742 Simplifying x = 33.899748742Subproblem 2
x + -14 = -19.899748742 Simplifying x + -14 = -19.899748742 Reorder the terms: -14 + x = -19.899748742 Solving -14 + x = -19.899748742 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '14' to each side of the equation. -14 + 14 + x = -19.899748742 + 14 Combine like terms: -14 + 14 = 0 0 + x = -19.899748742 + 14 x = -19.899748742 + 14 Combine like terms: -19.899748742 + 14 = -5.899748742 x = -5.899748742 Simplifying x = -5.899748742Solution
The solution to the problem is based on the solutions from the subproblems. x = {33.899748742, -5.899748742}
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