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Simplifying 2x2 + -7x = 320 Reorder the terms: -7x + 2x2 = 320 Solving -7x + 2x2 = 320 Solving for variable 'x'. Reorder the terms: -320 + -7x + 2x2 = 320 + -320 Combine like terms: 320 + -320 = 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 = 14.519592789 x = 14.519592789 Simplifying x = 14.519592789Subproblem 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 = -11.019592789 x = -11.019592789 Simplifying x = -11.019592789Solution
The solution to the problem is based on the solutions from the subproblems. x = {14.519592789, -11.019592789}
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