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Simplifying -1x2 + 40x + 300 = 0 Reorder the terms: 300 + 40x + -1x2 = 0 Solving 300 + 40x + -1x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -300 + -40x + x2 = 0 Move the constant term to the right: Add '300' to each side of the equation. -300 + -40x + 300 + x2 = 0 + 300 Reorder the terms: -300 + 300 + -40x + x2 = 0 + 300 Combine like terms: -300 + 300 = 0 0 + -40x + x2 = 0 + 300 -40x + x2 = 0 + 300 Combine like terms: 0 + 300 = 300 -40x + x2 = 300 The x term is -40x. Take half its coefficient (-20). Square it (400) and add it to both sides. Add '400' to each side of the equation. -40x + 400 + x2 = 300 + 400 Reorder the terms: 400 + -40x + x2 = 300 + 400 Combine like terms: 300 + 400 = 700 400 + -40x + x2 = 700 Factor a perfect square on the left side: (x + -20)(x + -20) = 700 Calculate the square root of the right side: 26.457513111 Break this problem into two subproblems by setting (x + -20) equal to 26.457513111 and -26.457513111.Subproblem 1
x + -20 = 26.457513111 Simplifying x + -20 = 26.457513111 Reorder the terms: -20 + x = 26.457513111 Solving -20 + x = 26.457513111 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '20' to each side of the equation. -20 + 20 + x = 26.457513111 + 20 Combine like terms: -20 + 20 = 0 0 + x = 26.457513111 + 20 x = 26.457513111 + 20 Combine like terms: 26.457513111 + 20 = 46.457513111 x = 46.457513111 Simplifying x = 46.457513111Subproblem 2
x + -20 = -26.457513111 Simplifying x + -20 = -26.457513111 Reorder the terms: -20 + x = -26.457513111 Solving -20 + x = -26.457513111 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '20' to each side of the equation. -20 + 20 + x = -26.457513111 + 20 Combine like terms: -20 + 20 = 0 0 + x = -26.457513111 + 20 x = -26.457513111 + 20 Combine like terms: -26.457513111 + 20 = -6.457513111 x = -6.457513111 Simplifying x = -6.457513111Solution
The solution to the problem is based on the solutions from the subproblems. x = {46.457513111, -6.457513111}
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