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Simplifying 0.5x2 + 14x + -10500 = 0 Reorder the terms: -10500 + 14x + 0.5x2 = 0 Solving -10500 + 14x + 0.5x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 0.5 the coefficient of the squared term: Divide each side by '0.5'. -21000 + 28x + x2 = 0 Move the constant term to the right: Add '21000' to each side of the equation. -21000 + 28x + 21000 + x2 = 0 + 21000 Reorder the terms: -21000 + 21000 + 28x + x2 = 0 + 21000 Combine like terms: -21000 + 21000 = 0 0 + 28x + x2 = 0 + 21000 28x + x2 = 0 + 21000 Combine like terms: 0 + 21000 = 21000 28x + x2 = 21000 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 = 21000 + 196 Reorder the terms: 196 + 28x + x2 = 21000 + 196 Combine like terms: 21000 + 196 = 21196 196 + 28x + x2 = 21196 Factor a perfect square on the left side: (x + 14)(x + 14) = 21196 Calculate the square root of the right side: 145.588461081 Break this problem into two subproblems by setting (x + 14) equal to 145.588461081 and -145.588461081.Subproblem 1
x + 14 = 145.588461081 Simplifying x + 14 = 145.588461081 Reorder the terms: 14 + x = 145.588461081 Solving 14 + x = 145.588461081 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 = 145.588461081 + -14 Combine like terms: 14 + -14 = 0 0 + x = 145.588461081 + -14 x = 145.588461081 + -14 Combine like terms: 145.588461081 + -14 = 131.588461081 x = 131.588461081 Simplifying x = 131.588461081Subproblem 2
x + 14 = -145.588461081 Simplifying x + 14 = -145.588461081 Reorder the terms: 14 + x = -145.588461081 Solving 14 + x = -145.588461081 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 = -145.588461081 + -14 Combine like terms: 14 + -14 = 0 0 + x = -145.588461081 + -14 x = -145.588461081 + -14 Combine like terms: -145.588461081 + -14 = -159.588461081 x = -159.588461081 Simplifying x = -159.588461081Solution
The solution to the problem is based on the solutions from the subproblems. x = {131.588461081, -159.588461081}
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