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Simplifying 0.5x2 + -7x = 16 Reorder the terms: -7x + 0.5x2 = 16 Solving -7x + 0.5x2 = 16 Solving for variable 'x'. Reorder the terms: -16 + -7x + 0.5x2 = 16 + -16 Combine like terms: 16 + -16 = 0 -16 + -7x + 0.5x2 = 0 Begin completing the square. Divide all terms by 0.5 the coefficient of the squared term: Divide each side by '0.5'. -32 + -14x + x2 = 0 Move the constant term to the right: Add '32' to each side of the equation. -32 + -14x + 32 + x2 = 0 + 32 Reorder the terms: -32 + 32 + -14x + x2 = 0 + 32 Combine like terms: -32 + 32 = 0 0 + -14x + x2 = 0 + 32 -14x + x2 = 0 + 32 Combine like terms: 0 + 32 = 32 -14x + x2 = 32 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 = 32 + 49 Reorder the terms: 49 + -14x + x2 = 32 + 49 Combine like terms: 32 + 49 = 81 49 + -14x + x2 = 81 Factor a perfect square on the left side: (x + -7)(x + -7) = 81 Calculate the square root of the right side: 9 Break this problem into two subproblems by setting (x + -7) equal to 9 and -9.Subproblem 1
x + -7 = 9 Simplifying x + -7 = 9 Reorder the terms: -7 + x = 9 Solving -7 + x = 9 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 = 9 + 7 Combine like terms: -7 + 7 = 0 0 + x = 9 + 7 x = 9 + 7 Combine like terms: 9 + 7 = 16 x = 16 Simplifying x = 16Subproblem 2
x + -7 = -9 Simplifying x + -7 = -9 Reorder the terms: -7 + x = -9 Solving -7 + x = -9 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 = -9 + 7 Combine like terms: -7 + 7 = 0 0 + x = -9 + 7 x = -9 + 7 Combine like terms: -9 + 7 = -2 x = -2 Simplifying x = -2Solution
The solution to the problem is based on the solutions from the subproblems. x = {16, -2}
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