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Simplifying 320 = x(2x + 7) Reorder the terms: 320 = x(7 + 2x) 320 = (7 * x + 2x * x) 320 = (7x + 2x2) Solving 320 = 7x + 2x2 Solving for variable 'x'. Reorder the terms: 320 + -7x + -2x2 = 7x + -7x + 2x2 + -2x2 Combine like terms: 7x + -7x = 0 320 + -7x + -2x2 = 0 + 2x2 + -2x2 320 + -7x + -2x2 = 2x2 + -2x2 Combine like terms: 2x2 + -2x2 = 0 320 + -7x + -2x2 = 0 Begin completing the square. Divide all terms by -2 the coefficient of the squared term: Divide each side by '-2'. -160 + 3.5x + x2 = 0 Move the constant term to the right: Add '160' to each side of the equation. -160 + 3.5x + 160 + x2 = 0 + 160 Reorder the terms: -160 + 160 + 3.5x + x2 = 0 + 160 Combine like terms: -160 + 160 = 0 0 + 3.5x + x2 = 0 + 160 3.5x + x2 = 0 + 160 Combine like terms: 0 + 160 = 160 3.5x + x2 = 160 The x term is 3.5x. Take half its coefficient (1.75). Square it (3.0625) and add it to both sides. Add '3.0625' to each side of the equation. 3.5x + 3.0625 + x2 = 160 + 3.0625 Reorder the terms: 3.0625 + 3.5x + x2 = 160 + 3.0625 Combine like terms: 160 + 3.0625 = 163.0625 3.0625 + 3.5x + x2 = 163.0625 Factor a perfect square on the left side: (x + 1.75)(x + 1.75) = 163.0625 Calculate the square root of the right side: 12.769592789 Break this problem into two subproblems by setting (x + 1.75) equal to 12.769592789 and -12.769592789.Subproblem 1
x + 1.75 = 12.769592789 Simplifying x + 1.75 = 12.769592789 Reorder the terms: 1.75 + x = 12.769592789 Solving 1.75 + x = 12.769592789 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.75' to each side of the equation. 1.75 + -1.75 + x = 12.769592789 + -1.75 Combine like terms: 1.75 + -1.75 = 0.00 0.00 + x = 12.769592789 + -1.75 x = 12.769592789 + -1.75 Combine like terms: 12.769592789 + -1.75 = 11.019592789 x = 11.019592789 Simplifying x = 11.019592789Subproblem 2
x + 1.75 = -12.769592789 Simplifying x + 1.75 = -12.769592789 Reorder the terms: 1.75 + x = -12.769592789 Solving 1.75 + x = -12.769592789 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.75' to each side of the equation. 1.75 + -1.75 + x = -12.769592789 + -1.75 Combine like terms: 1.75 + -1.75 = 0.00 0.00 + x = -12.769592789 + -1.75 x = -12.769592789 + -1.75 Combine like terms: -12.769592789 + -1.75 = -14.519592789 x = -14.519592789 Simplifying x = -14.519592789Solution
The solution to the problem is based on the solutions from the subproblems. x = {11.019592789, -14.519592789}
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