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Simplifying -1.8x2 + 9.4x + 7 = 0 Reorder the terms: 7 + 9.4x + -1.8x2 = 0 Solving 7 + 9.4x + -1.8x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by -1.8 the coefficient of the squared term: Divide each side by '-1.8'. -3.888888889 + -5.222222222x + x2 = 0 Move the constant term to the right: Add '3.888888889' to each side of the equation. -3.888888889 + -5.222222222x + 3.888888889 + x2 = 0 + 3.888888889 Reorder the terms: -3.888888889 + 3.888888889 + -5.222222222x + x2 = 0 + 3.888888889 Combine like terms: -3.888888889 + 3.888888889 = 0.000000000 0.000000000 + -5.222222222x + x2 = 0 + 3.888888889 -5.222222222x + x2 = 0 + 3.888888889 Combine like terms: 0 + 3.888888889 = 3.888888889 -5.222222222x + x2 = 3.888888889 The x term is -5.222222222x. Take half its coefficient (-2.611111111). Square it (6.817901234) and add it to both sides. Add '6.817901234' to each side of the equation. -5.222222222x + 6.817901234 + x2 = 3.888888889 + 6.817901234 Reorder the terms: 6.817901234 + -5.222222222x + x2 = 3.888888889 + 6.817901234 Combine like terms: 3.888888889 + 6.817901234 = 10.706790123 6.817901234 + -5.222222222x + x2 = 10.706790123 Factor a perfect square on the left side: (x + -2.611111111)(x + -2.611111111) = 10.706790123 Calculate the square root of the right side: 3.272123183 Break this problem into two subproblems by setting (x + -2.611111111) equal to 3.272123183 and -3.272123183.Subproblem 1
x + -2.611111111 = 3.272123183 Simplifying x + -2.611111111 = 3.272123183 Reorder the terms: -2.611111111 + x = 3.272123183 Solving -2.611111111 + x = 3.272123183 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.611111111' to each side of the equation. -2.611111111 + 2.611111111 + x = 3.272123183 + 2.611111111 Combine like terms: -2.611111111 + 2.611111111 = 0.000000000 0.000000000 + x = 3.272123183 + 2.611111111 x = 3.272123183 + 2.611111111 Combine like terms: 3.272123183 + 2.611111111 = 5.883234294 x = 5.883234294 Simplifying x = 5.883234294Subproblem 2
x + -2.611111111 = -3.272123183 Simplifying x + -2.611111111 = -3.272123183 Reorder the terms: -2.611111111 + x = -3.272123183 Solving -2.611111111 + x = -3.272123183 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.611111111' to each side of the equation. -2.611111111 + 2.611111111 + x = -3.272123183 + 2.611111111 Combine like terms: -2.611111111 + 2.611111111 = 0.000000000 0.000000000 + x = -3.272123183 + 2.611111111 x = -3.272123183 + 2.611111111 Combine like terms: -3.272123183 + 2.611111111 = -0.661012072 x = -0.661012072 Simplifying x = -0.661012072Solution
The solution to the problem is based on the solutions from the subproblems. x = {5.883234294, -0.661012072}
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