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Simplifying 7x + -6 = 0.5(36 + x2) Reorder the terms: -6 + 7x = 0.5(36 + x2) -6 + 7x = (36 * 0.5 + x2 * 0.5) -6 + 7x = (18 + 0.5x2) Solving -6 + 7x = 18 + 0.5x2 Solving for variable 'x'. Reorder the terms: -6 + -18 + 7x + -0.5x2 = 18 + 0.5x2 + -18 + -0.5x2 Combine like terms: -6 + -18 = -24 -24 + 7x + -0.5x2 = 18 + 0.5x2 + -18 + -0.5x2 Reorder the terms: -24 + 7x + -0.5x2 = 18 + -18 + 0.5x2 + -0.5x2 Combine like terms: 18 + -18 = 0 -24 + 7x + -0.5x2 = 0 + 0.5x2 + -0.5x2 -24 + 7x + -0.5x2 = 0.5x2 + -0.5x2 Combine like terms: 0.5x2 + -0.5x2 = 0.0 -24 + 7x + -0.5x2 = 0.0 Begin completing the square. Divide all terms by -0.5 the coefficient of the squared term: Divide each side by '-0.5'. 48 + -14x + x2 = 0 Move the constant term to the right: Add '-48' to each side of the equation. 48 + -14x + -48 + x2 = 0 + -48 Reorder the terms: 48 + -48 + -14x + x2 = 0 + -48 Combine like terms: 48 + -48 = 0 0 + -14x + x2 = 0 + -48 -14x + x2 = 0 + -48 Combine like terms: 0 + -48 = -48 -14x + x2 = -48 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 = -48 + 49 Reorder the terms: 49 + -14x + x2 = -48 + 49 Combine like terms: -48 + 49 = 1 49 + -14x + x2 = 1 Factor a perfect square on the left side: (x + -7)(x + -7) = 1 Calculate the square root of the right side: 1 Break this problem into two subproblems by setting (x + -7) equal to 1 and -1.Subproblem 1
x + -7 = 1 Simplifying x + -7 = 1 Reorder the terms: -7 + x = 1 Solving -7 + x = 1 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 = 1 + 7 Combine like terms: -7 + 7 = 0 0 + x = 1 + 7 x = 1 + 7 Combine like terms: 1 + 7 = 8 x = 8 Simplifying x = 8Subproblem 2
x + -7 = -1 Simplifying x + -7 = -1 Reorder the terms: -7 + x = -1 Solving -7 + x = -1 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 = -1 + 7 Combine like terms: -7 + 7 = 0 0 + x = -1 + 7 x = -1 + 7 Combine like terms: -1 + 7 = 6 x = 6 Simplifying x = 6Solution
The solution to the problem is based on the solutions from the subproblems. x = {8, 6}
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