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Simplifying 5x2 + -7x + -40 = 0 Reorder the terms: -40 + -7x + 5x2 = 0 Solving -40 + -7x + 5x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 5 the coefficient of the squared term: Divide each side by '5'. -8 + -1.4x + x2 = 0 Move the constant term to the right: Add '8' to each side of the equation. -8 + -1.4x + 8 + x2 = 0 + 8 Reorder the terms: -8 + 8 + -1.4x + x2 = 0 + 8 Combine like terms: -8 + 8 = 0 0 + -1.4x + x2 = 0 + 8 -1.4x + x2 = 0 + 8 Combine like terms: 0 + 8 = 8 -1.4x + x2 = 8 The x term is -1.4x. Take half its coefficient (-0.7). Square it (0.49) and add it to both sides. Add '0.49' to each side of the equation. -1.4x + 0.49 + x2 = 8 + 0.49 Reorder the terms: 0.49 + -1.4x + x2 = 8 + 0.49 Combine like terms: 8 + 0.49 = 8.49 0.49 + -1.4x + x2 = 8.49 Factor a perfect square on the left side: (x + -0.7)(x + -0.7) = 8.49 Calculate the square root of the right side: 2.913760457 Break this problem into two subproblems by setting (x + -0.7) equal to 2.913760457 and -2.913760457.Subproblem 1
x + -0.7 = 2.913760457 Simplifying x + -0.7 = 2.913760457 Reorder the terms: -0.7 + x = 2.913760457 Solving -0.7 + x = 2.913760457 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.7' to each side of the equation. -0.7 + 0.7 + x = 2.913760457 + 0.7 Combine like terms: -0.7 + 0.7 = 0.0 0.0 + x = 2.913760457 + 0.7 x = 2.913760457 + 0.7 Combine like terms: 2.913760457 + 0.7 = 3.613760457 x = 3.613760457 Simplifying x = 3.613760457Subproblem 2
x + -0.7 = -2.913760457 Simplifying x + -0.7 = -2.913760457 Reorder the terms: -0.7 + x = -2.913760457 Solving -0.7 + x = -2.913760457 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.7' to each side of the equation. -0.7 + 0.7 + x = -2.913760457 + 0.7 Combine like terms: -0.7 + 0.7 = 0.0 0.0 + x = -2.913760457 + 0.7 x = -2.913760457 + 0.7 Combine like terms: -2.913760457 + 0.7 = -2.213760457 x = -2.213760457 Simplifying x = -2.213760457Solution
The solution to the problem is based on the solutions from the subproblems. x = {3.613760457, -2.213760457}
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