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Simplifying -5x2 + 28x + 40 = 0 Reorder the terms: 40 + 28x + -5x2 = 0 Solving 40 + 28x + -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 + -5.6x + x2 = 0 Move the constant term to the right: Add '8' to each side of the equation. -8 + -5.6x + 8 + x2 = 0 + 8 Reorder the terms: -8 + 8 + -5.6x + x2 = 0 + 8 Combine like terms: -8 + 8 = 0 0 + -5.6x + x2 = 0 + 8 -5.6x + x2 = 0 + 8 Combine like terms: 0 + 8 = 8 -5.6x + x2 = 8 The x term is -5.6x. Take half its coefficient (-2.8). Square it (7.84) and add it to both sides. Add '7.84' to each side of the equation. -5.6x + 7.84 + x2 = 8 + 7.84 Reorder the terms: 7.84 + -5.6x + x2 = 8 + 7.84 Combine like terms: 8 + 7.84 = 15.84 7.84 + -5.6x + x2 = 15.84 Factor a perfect square on the left side: (x + -2.8)(x + -2.8) = 15.84 Calculate the square root of the right side: 3.979949748 Break this problem into two subproblems by setting (x + -2.8) equal to 3.979949748 and -3.979949748.Subproblem 1
x + -2.8 = 3.979949748 Simplifying x + -2.8 = 3.979949748 Reorder the terms: -2.8 + x = 3.979949748 Solving -2.8 + x = 3.979949748 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.8' to each side of the equation. -2.8 + 2.8 + x = 3.979949748 + 2.8 Combine like terms: -2.8 + 2.8 = 0.0 0.0 + x = 3.979949748 + 2.8 x = 3.979949748 + 2.8 Combine like terms: 3.979949748 + 2.8 = 6.779949748 x = 6.779949748 Simplifying x = 6.779949748Subproblem 2
x + -2.8 = -3.979949748 Simplifying x + -2.8 = -3.979949748 Reorder the terms: -2.8 + x = -3.979949748 Solving -2.8 + x = -3.979949748 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.8' to each side of the equation. -2.8 + 2.8 + x = -3.979949748 + 2.8 Combine like terms: -2.8 + 2.8 = 0.0 0.0 + x = -3.979949748 + 2.8 x = -3.979949748 + 2.8 Combine like terms: -3.979949748 + 2.8 = -1.179949748 x = -1.179949748 Simplifying x = -1.179949748Solution
The solution to the problem is based on the solutions from the subproblems. x = {6.779949748, -1.179949748}
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