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Simplifying 7.67x2 + 2.73x + -5.33 = 0 Reorder the terms: -5.33 + 2.73x + 7.67x2 = 0 Solving -5.33 + 2.73x + 7.67x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 7.67 the coefficient of the squared term: Divide each side by '7.67'. -0.6949152542 + 0.3559322034x + x2 = 0 Move the constant term to the right: Add '0.6949152542' to each side of the equation. -0.6949152542 + 0.3559322034x + 0.6949152542 + x2 = 0 + 0.6949152542 Reorder the terms: -0.6949152542 + 0.6949152542 + 0.3559322034x + x2 = 0 + 0.6949152542 Combine like terms: -0.6949152542 + 0.6949152542 = 0.0000000000 0.0000000000 + 0.3559322034x + x2 = 0 + 0.6949152542 0.3559322034x + x2 = 0 + 0.6949152542 Combine like terms: 0 + 0.6949152542 = 0.6949152542 0.3559322034x + x2 = 0.6949152542 The x term is 0.3559322034x. Take half its coefficient (0.1779661017). Square it (0.03167193335) and add it to both sides. Add '0.03167193335' to each side of the equation. 0.3559322034x + 0.03167193335 + x2 = 0.6949152542 + 0.03167193335 Reorder the terms: 0.03167193335 + 0.3559322034x + x2 = 0.6949152542 + 0.03167193335 Combine like terms: 0.6949152542 + 0.03167193335 = 0.72658718755 0.03167193335 + 0.3559322034x + x2 = 0.72658718755 Factor a perfect square on the left side: (x + 0.1779661017)(x + 0.1779661017) = 0.72658718755 Calculate the square root of the right side: 0.852400837 Break this problem into two subproblems by setting (x + 0.1779661017) equal to 0.852400837 and -0.852400837.Subproblem 1
x + 0.1779661017 = 0.852400837 Simplifying x + 0.1779661017 = 0.852400837 Reorder the terms: 0.1779661017 + x = 0.852400837 Solving 0.1779661017 + x = 0.852400837 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.1779661017' to each side of the equation. 0.1779661017 + -0.1779661017 + x = 0.852400837 + -0.1779661017 Combine like terms: 0.1779661017 + -0.1779661017 = 0.0000000000 0.0000000000 + x = 0.852400837 + -0.1779661017 x = 0.852400837 + -0.1779661017 Combine like terms: 0.852400837 + -0.1779661017 = 0.6744347353 x = 0.6744347353 Simplifying x = 0.6744347353Subproblem 2
x + 0.1779661017 = -0.852400837 Simplifying x + 0.1779661017 = -0.852400837 Reorder the terms: 0.1779661017 + x = -0.852400837 Solving 0.1779661017 + x = -0.852400837 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.1779661017' to each side of the equation. 0.1779661017 + -0.1779661017 + x = -0.852400837 + -0.1779661017 Combine like terms: 0.1779661017 + -0.1779661017 = 0.0000000000 0.0000000000 + x = -0.852400837 + -0.1779661017 x = -0.852400837 + -0.1779661017 Combine like terms: -0.852400837 + -0.1779661017 = -1.0303669387 x = -1.0303669387 Simplifying x = -1.0303669387Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.6744347353, -1.0303669387}
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