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Simplifying 1.2x2 + 1.2x = 66 Reorder the terms: 1.2x + 1.2x2 = 66 Solving 1.2x + 1.2x2 = 66 Solving for variable 'x'. Reorder the terms: -66 + 1.2x + 1.2x2 = 66 + -66 Combine like terms: 66 + -66 = 0 -66 + 1.2x + 1.2x2 = 0 Begin completing the square. Divide all terms by 1.2 the coefficient of the squared term: Divide each side by '1.2'. -55 + x + x2 = 0 Move the constant term to the right: Add '55' to each side of the equation. -55 + x + 55 + x2 = 0 + 55 Reorder the terms: -55 + 55 + x + x2 = 0 + 55 Combine like terms: -55 + 55 = 0 0 + x + x2 = 0 + 55 x + x2 = 0 + 55 Combine like terms: 0 + 55 = 55 x + x2 = 55 The x term is x. Take half its coefficient (0.5). Square it (0.25) and add it to both sides. Add '0.25' to each side of the equation. + 0.25 + x2 = 55 + 0.25 Combine like terms: + 0.25 = 1.25 1.25 + x2 = 55 + 0.25 Combine like terms: 55 + 0.25 = 55.25 1.25 + x2 = 55.25 Factor a perfect square on the left side: (x + 0.5)(x + 0.5) = 55.25 Calculate the square root of the right side: 7.433034374 Break this problem into two subproblems by setting (x + 0.5) equal to 7.433034374 and -7.433034374.Subproblem 1
x + 0.5 = 7.433034374 Simplifying x + 0.5 = 7.433034374 Reorder the terms: 0.5 + x = 7.433034374 Solving 0.5 + x = 7.433034374 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.5' to each side of the equation. 0.5 + -0.5 + x = 7.433034374 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x = 7.433034374 + -0.5 x = 7.433034374 + -0.5 Combine like terms: 7.433034374 + -0.5 = 6.933034374 x = 6.933034374 Simplifying x = 6.933034374Subproblem 2
x + 0.5 = -7.433034374 Simplifying x + 0.5 = -7.433034374 Reorder the terms: 0.5 + x = -7.433034374 Solving 0.5 + x = -7.433034374 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.5' to each side of the equation. 0.5 + -0.5 + x = -7.433034374 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x = -7.433034374 + -0.5 x = -7.433034374 + -0.5 Combine like terms: -7.433034374 + -0.5 = -7.933034374 x = -7.933034374 Simplifying x = -7.933034374Solution
The solution to the problem is based on the solutions from the subproblems. x = {6.933034374, -7.933034374}
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