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Simplifying 20x2 + 35x + -10 = 8 Reorder the terms: -10 + 35x + 20x2 = 8 Solving -10 + 35x + 20x2 = 8 Solving for variable 'x'. Reorder the terms: -10 + -8 + 35x + 20x2 = 8 + -8 Combine like terms: -10 + -8 = -18 -18 + 35x + 20x2 = 8 + -8 Combine like terms: 8 + -8 = 0 -18 + 35x + 20x2 = 0 Begin completing the square. Divide all terms by 20 the coefficient of the squared term: Divide each side by '20'. -0.9 + 1.75x + x2 = 0 Move the constant term to the right: Add '0.9' to each side of the equation. -0.9 + 1.75x + 0.9 + x2 = 0 + 0.9 Reorder the terms: -0.9 + 0.9 + 1.75x + x2 = 0 + 0.9 Combine like terms: -0.9 + 0.9 = 0.0 0.0 + 1.75x + x2 = 0 + 0.9 1.75x + x2 = 0 + 0.9 Combine like terms: 0 + 0.9 = 0.9 1.75x + x2 = 0.9 The x term is 1.75x. Take half its coefficient (0.875). Square it (0.765625) and add it to both sides. Add '0.765625' to each side of the equation. 1.75x + 0.765625 + x2 = 0.9 + 0.765625 Reorder the terms: 0.765625 + 1.75x + x2 = 0.9 + 0.765625 Combine like terms: 0.9 + 0.765625 = 1.665625 0.765625 + 1.75x + x2 = 1.665625 Factor a perfect square on the left side: (x + 0.875)(x + 0.875) = 1.665625 Calculate the square root of the right side: 1.29059095 Break this problem into two subproblems by setting (x + 0.875) equal to 1.29059095 and -1.29059095.Subproblem 1
x + 0.875 = 1.29059095 Simplifying x + 0.875 = 1.29059095 Reorder the terms: 0.875 + x = 1.29059095 Solving 0.875 + x = 1.29059095 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.875' to each side of the equation. 0.875 + -0.875 + x = 1.29059095 + -0.875 Combine like terms: 0.875 + -0.875 = 0.000 0.000 + x = 1.29059095 + -0.875 x = 1.29059095 + -0.875 Combine like terms: 1.29059095 + -0.875 = 0.41559095 x = 0.41559095 Simplifying x = 0.41559095Subproblem 2
x + 0.875 = -1.29059095 Simplifying x + 0.875 = -1.29059095 Reorder the terms: 0.875 + x = -1.29059095 Solving 0.875 + x = -1.29059095 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.875' to each side of the equation. 0.875 + -0.875 + x = -1.29059095 + -0.875 Combine like terms: 0.875 + -0.875 = 0.000 0.000 + x = -1.29059095 + -0.875 x = -1.29059095 + -0.875 Combine like terms: -1.29059095 + -0.875 = -2.16559095 x = -2.16559095 Simplifying x = -2.16559095Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.41559095, -2.16559095}
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