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Simplifying 5x2 = 7 + -40x Solving 5x2 = 7 + -40x Solving for variable 'x'. Reorder the terms: -7 + 40x + 5x2 = 7 + -40x + -7 + 40x Reorder the terms: -7 + 40x + 5x2 = 7 + -7 + -40x + 40x Combine like terms: 7 + -7 = 0 -7 + 40x + 5x2 = 0 + -40x + 40x -7 + 40x + 5x2 = -40x + 40x Combine like terms: -40x + 40x = 0 -7 + 40x + 5x2 = 0 Begin completing the square. Divide all terms by 5 the coefficient of the squared term: Divide each side by '5'. -1.4 + 8x + x2 = 0 Move the constant term to the right: Add '1.4' to each side of the equation. -1.4 + 8x + 1.4 + x2 = 0 + 1.4 Reorder the terms: -1.4 + 1.4 + 8x + x2 = 0 + 1.4 Combine like terms: -1.4 + 1.4 = 0.0 0.0 + 8x + x2 = 0 + 1.4 8x + x2 = 0 + 1.4 Combine like terms: 0 + 1.4 = 1.4 8x + x2 = 1.4 The x term is 8x. Take half its coefficient (4). Square it (16) and add it to both sides. Add '16' to each side of the equation. 8x + 16 + x2 = 1.4 + 16 Reorder the terms: 16 + 8x + x2 = 1.4 + 16 Combine like terms: 1.4 + 16 = 17.4 16 + 8x + x2 = 17.4 Factor a perfect square on the left side: (x + 4)(x + 4) = 17.4 Calculate the square root of the right side: 4.171330723 Break this problem into two subproblems by setting (x + 4) equal to 4.171330723 and -4.171330723.Subproblem 1
x + 4 = 4.171330723 Simplifying x + 4 = 4.171330723 Reorder the terms: 4 + x = 4.171330723 Solving 4 + x = 4.171330723 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-4' to each side of the equation. 4 + -4 + x = 4.171330723 + -4 Combine like terms: 4 + -4 = 0 0 + x = 4.171330723 + -4 x = 4.171330723 + -4 Combine like terms: 4.171330723 + -4 = 0.171330723 x = 0.171330723 Simplifying x = 0.171330723Subproblem 2
x + 4 = -4.171330723 Simplifying x + 4 = -4.171330723 Reorder the terms: 4 + x = -4.171330723 Solving 4 + x = -4.171330723 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-4' to each side of the equation. 4 + -4 + x = -4.171330723 + -4 Combine like terms: 4 + -4 = 0 0 + x = -4.171330723 + -4 x = -4.171330723 + -4 Combine like terms: -4.171330723 + -4 = -8.171330723 x = -8.171330723 Simplifying x = -8.171330723Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.171330723, -8.171330723}
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