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Simplifying 5x2 + 8x + -11 = 7 Reorder the terms: -11 + 8x + 5x2 = 7 Solving -11 + 8x + 5x2 = 7 Solving for variable 'x'. Reorder the terms: -11 + -7 + 8x + 5x2 = 7 + -7 Combine like terms: -11 + -7 = -18 -18 + 8x + 5x2 = 7 + -7 Combine like terms: 7 + -7 = 0 -18 + 8x + 5x2 = 0 Begin completing the square. Divide all terms by 5 the coefficient of the squared term: Divide each side by '5'. -3.6 + 1.6x + x2 = 0 Move the constant term to the right: Add '3.6' to each side of the equation. -3.6 + 1.6x + 3.6 + x2 = 0 + 3.6 Reorder the terms: -3.6 + 3.6 + 1.6x + x2 = 0 + 3.6 Combine like terms: -3.6 + 3.6 = 0.0 0.0 + 1.6x + x2 = 0 + 3.6 1.6x + x2 = 0 + 3.6 Combine like terms: 0 + 3.6 = 3.6 1.6x + x2 = 3.6 The x term is 1.6x. Take half its coefficient (0.8). Square it (0.64) and add it to both sides. Add '0.64' to each side of the equation. 1.6x + 0.64 + x2 = 3.6 + 0.64 Reorder the terms: 0.64 + 1.6x + x2 = 3.6 + 0.64 Combine like terms: 3.6 + 0.64 = 4.24 0.64 + 1.6x + x2 = 4.24 Factor a perfect square on the left side: (x + 0.8)(x + 0.8) = 4.24 Calculate the square root of the right side: 2.059126028 Break this problem into two subproblems by setting (x + 0.8) equal to 2.059126028 and -2.059126028.Subproblem 1
x + 0.8 = 2.059126028 Simplifying x + 0.8 = 2.059126028 Reorder the terms: 0.8 + x = 2.059126028 Solving 0.8 + x = 2.059126028 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.8' to each side of the equation. 0.8 + -0.8 + x = 2.059126028 + -0.8 Combine like terms: 0.8 + -0.8 = 0.0 0.0 + x = 2.059126028 + -0.8 x = 2.059126028 + -0.8 Combine like terms: 2.059126028 + -0.8 = 1.259126028 x = 1.259126028 Simplifying x = 1.259126028Subproblem 2
x + 0.8 = -2.059126028 Simplifying x + 0.8 = -2.059126028 Reorder the terms: 0.8 + x = -2.059126028 Solving 0.8 + x = -2.059126028 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.8' to each side of the equation. 0.8 + -0.8 + x = -2.059126028 + -0.8 Combine like terms: 0.8 + -0.8 = 0.0 0.0 + x = -2.059126028 + -0.8 x = -2.059126028 + -0.8 Combine like terms: -2.059126028 + -0.8 = -2.859126028 x = -2.859126028 Simplifying x = -2.859126028Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.259126028, -2.859126028}
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