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Simplifying 2x2 + 2.4x + -80 = 0 Reorder the terms: -80 + 2.4x + 2x2 = 0 Solving -80 + 2.4x + 2x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. -40 + 1.2x + x2 = 0 Move the constant term to the right: Add '40' to each side of the equation. -40 + 1.2x + 40 + x2 = 0 + 40 Reorder the terms: -40 + 40 + 1.2x + x2 = 0 + 40 Combine like terms: -40 + 40 = 0 0 + 1.2x + x2 = 0 + 40 1.2x + x2 = 0 + 40 Combine like terms: 0 + 40 = 40 1.2x + x2 = 40 The x term is 1.2x. Take half its coefficient (0.6). Square it (0.36) and add it to both sides. Add '0.36' to each side of the equation. 1.2x + 0.36 + x2 = 40 + 0.36 Reorder the terms: 0.36 + 1.2x + x2 = 40 + 0.36 Combine like terms: 40 + 0.36 = 40.36 0.36 + 1.2x + x2 = 40.36 Factor a perfect square on the left side: (x + 0.6)(x + 0.6) = 40.36 Calculate the square root of the right side: 6.35295207 Break this problem into two subproblems by setting (x + 0.6) equal to 6.35295207 and -6.35295207.Subproblem 1
x + 0.6 = 6.35295207 Simplifying x + 0.6 = 6.35295207 Reorder the terms: 0.6 + x = 6.35295207 Solving 0.6 + x = 6.35295207 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.6' to each side of the equation. 0.6 + -0.6 + x = 6.35295207 + -0.6 Combine like terms: 0.6 + -0.6 = 0.0 0.0 + x = 6.35295207 + -0.6 x = 6.35295207 + -0.6 Combine like terms: 6.35295207 + -0.6 = 5.75295207 x = 5.75295207 Simplifying x = 5.75295207Subproblem 2
x + 0.6 = -6.35295207 Simplifying x + 0.6 = -6.35295207 Reorder the terms: 0.6 + x = -6.35295207 Solving 0.6 + x = -6.35295207 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.6' to each side of the equation. 0.6 + -0.6 + x = -6.35295207 + -0.6 Combine like terms: 0.6 + -0.6 = 0.0 0.0 + x = -6.35295207 + -0.6 x = -6.35295207 + -0.6 Combine like terms: -6.35295207 + -0.6 = -6.95295207 x = -6.95295207 Simplifying x = -6.95295207Solution
The solution to the problem is based on the solutions from the subproblems. x = {5.75295207, -6.95295207}
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