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Simplifying 7.7x(x + -2) = -0.3 + 48.6 Reorder the terms: 7.7x(-2 + x) = -0.3 + 48.6 (-2 * 7.7x + x * 7.7x) = -0.3 + 48.6 (-15.4x + 7.7x2) = -0.3 + 48.6 Combine like terms: -0.3 + 48.6 = 48.3 -15.4x + 7.7x2 = 48.3 Solving -15.4x + 7.7x2 = 48.3 Solving for variable 'x'. Reorder the terms: -48.3 + -15.4x + 7.7x2 = 48.3 + -48.3 Combine like terms: 48.3 + -48.3 = 0.0 -48.3 + -15.4x + 7.7x2 = 0.0 Begin completing the square. Divide all terms by 7.7 the coefficient of the squared term: Divide each side by '7.7'. -6.272727273 + -2x + x2 = 0 Move the constant term to the right: Add '6.272727273' to each side of the equation. -6.272727273 + -2x + 6.272727273 + x2 = 0 + 6.272727273 Reorder the terms: -6.272727273 + 6.272727273 + -2x + x2 = 0 + 6.272727273 Combine like terms: -6.272727273 + 6.272727273 = 0.000000000 0.000000000 + -2x + x2 = 0 + 6.272727273 -2x + x2 = 0 + 6.272727273 Combine like terms: 0 + 6.272727273 = 6.272727273 -2x + x2 = 6.272727273 The x term is -2x. Take half its coefficient (-1). Square it (1) and add it to both sides. Add '1' to each side of the equation. -2x + 1 + x2 = 6.272727273 + 1 Reorder the terms: 1 + -2x + x2 = 6.272727273 + 1 Combine like terms: 6.272727273 + 1 = 7.272727273 1 + -2x + x2 = 7.272727273 Factor a perfect square on the left side: (x + -1)(x + -1) = 7.272727273 Calculate the square root of the right side: 2.69679945 Break this problem into two subproblems by setting (x + -1) equal to 2.69679945 and -2.69679945.Subproblem 1
x + -1 = 2.69679945 Simplifying x + -1 = 2.69679945 Reorder the terms: -1 + x = 2.69679945 Solving -1 + x = 2.69679945 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1' to each side of the equation. -1 + 1 + x = 2.69679945 + 1 Combine like terms: -1 + 1 = 0 0 + x = 2.69679945 + 1 x = 2.69679945 + 1 Combine like terms: 2.69679945 + 1 = 3.69679945 x = 3.69679945 Simplifying x = 3.69679945Subproblem 2
x + -1 = -2.69679945 Simplifying x + -1 = -2.69679945 Reorder the terms: -1 + x = -2.69679945 Solving -1 + x = -2.69679945 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1' to each side of the equation. -1 + 1 + x = -2.69679945 + 1 Combine like terms: -1 + 1 = 0 0 + x = -2.69679945 + 1 x = -2.69679945 + 1 Combine like terms: -2.69679945 + 1 = -1.69679945 x = -1.69679945 Simplifying x = -1.69679945Solution
The solution to the problem is based on the solutions from the subproblems. x = {3.69679945, -1.69679945}
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