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Simplifying 11x2 + -28x + -7 = 0 Reorder the terms: -7 + -28x + 11x2 = 0 Solving -7 + -28x + 11x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 11 the coefficient of the squared term: Divide each side by '11'. -0.6363636364 + -2.545454545x + x2 = 0 Move the constant term to the right: Add '0.6363636364' to each side of the equation. -0.6363636364 + -2.545454545x + 0.6363636364 + x2 = 0 + 0.6363636364 Reorder the terms: -0.6363636364 + 0.6363636364 + -2.545454545x + x2 = 0 + 0.6363636364 Combine like terms: -0.6363636364 + 0.6363636364 = 0.0000000000 0.0000000000 + -2.545454545x + x2 = 0 + 0.6363636364 -2.545454545x + x2 = 0 + 0.6363636364 Combine like terms: 0 + 0.6363636364 = 0.6363636364 -2.545454545x + x2 = 0.6363636364 The x term is -2.545454545x. Take half its coefficient (-1.272727273). Square it (1.619834711) and add it to both sides. Add '1.619834711' to each side of the equation. -2.545454545x + 1.619834711 + x2 = 0.6363636364 + 1.619834711 Reorder the terms: 1.619834711 + -2.545454545x + x2 = 0.6363636364 + 1.619834711 Combine like terms: 0.6363636364 + 1.619834711 = 2.2561983474 1.619834711 + -2.545454545x + x2 = 2.2561983474 Factor a perfect square on the left side: (x + -1.272727273)(x + -1.272727273) = 2.2561983474 Calculate the square root of the right side: 1.502064695 Break this problem into two subproblems by setting (x + -1.272727273) equal to 1.502064695 and -1.502064695.Subproblem 1
x + -1.272727273 = 1.502064695 Simplifying x + -1.272727273 = 1.502064695 Reorder the terms: -1.272727273 + x = 1.502064695 Solving -1.272727273 + x = 1.502064695 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.272727273' to each side of the equation. -1.272727273 + 1.272727273 + x = 1.502064695 + 1.272727273 Combine like terms: -1.272727273 + 1.272727273 = 0.000000000 0.000000000 + x = 1.502064695 + 1.272727273 x = 1.502064695 + 1.272727273 Combine like terms: 1.502064695 + 1.272727273 = 2.774791968 x = 2.774791968 Simplifying x = 2.774791968Subproblem 2
x + -1.272727273 = -1.502064695 Simplifying x + -1.272727273 = -1.502064695 Reorder the terms: -1.272727273 + x = -1.502064695 Solving -1.272727273 + x = -1.502064695 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.272727273' to each side of the equation. -1.272727273 + 1.272727273 + x = -1.502064695 + 1.272727273 Combine like terms: -1.272727273 + 1.272727273 = 0.000000000 0.000000000 + x = -1.502064695 + 1.272727273 x = -1.502064695 + 1.272727273 Combine like terms: -1.502064695 + 1.272727273 = -0.229337422 x = -0.229337422 Simplifying x = -0.229337422Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.774791968, -0.229337422}
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