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Simplifying -0.04x2 + 8.4x + -245 = 0 Reorder the terms: -245 + 8.4x + -0.04x2 = 0 Solving -245 + 8.4x + -0.04x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by -0.04 the coefficient of the squared term: Divide each side by '-0.04'. 6125 + -210x + x2 = 0 Move the constant term to the right: Add '-6125' to each side of the equation. 6125 + -210x + -6125 + x2 = 0 + -6125 Reorder the terms: 6125 + -6125 + -210x + x2 = 0 + -6125 Combine like terms: 6125 + -6125 = 0 0 + -210x + x2 = 0 + -6125 -210x + x2 = 0 + -6125 Combine like terms: 0 + -6125 = -6125 -210x + x2 = -6125 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 = -6125 + 11025 Reorder the terms: 11025 + -210x + x2 = -6125 + 11025 Combine like terms: -6125 + 11025 = 4900 11025 + -210x + x2 = 4900 Factor a perfect square on the left side: (x + -105)(x + -105) = 4900 Calculate the square root of the right side: 70 Break this problem into two subproblems by setting (x + -105) equal to 70 and -70.Subproblem 1
x + -105 = 70 Simplifying x + -105 = 70 Reorder the terms: -105 + x = 70 Solving -105 + x = 70 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 = 70 + 105 Combine like terms: -105 + 105 = 0 0 + x = 70 + 105 x = 70 + 105 Combine like terms: 70 + 105 = 175 x = 175 Simplifying x = 175Subproblem 2
x + -105 = -70 Simplifying x + -105 = -70 Reorder the terms: -105 + x = -70 Solving -105 + x = -70 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 = -70 + 105 Combine like terms: -105 + 105 = 0 0 + x = -70 + 105 x = -70 + 105 Combine like terms: -70 + 105 = 35 x = 35 Simplifying x = 35Solution
The solution to the problem is based on the solutions from the subproblems. x = {175, 35}
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