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Simplifying -5.9x + 4.9x2 = 111 Solving -5.9x + 4.9x2 = 111 Solving for variable 'x'. Reorder the terms: -111 + -5.9x + 4.9x2 = 111 + -111 Combine like terms: 111 + -111 = 0 -111 + -5.9x + 4.9x2 = 0 Begin completing the square. Divide all terms by 4.9 the coefficient of the squared term: Divide each side by '4.9'. -22.65306122 + -1.204081633x + x2 = 0 Move the constant term to the right: Add '22.65306122' to each side of the equation. -22.65306122 + -1.204081633x + 22.65306122 + x2 = 0 + 22.65306122 Reorder the terms: -22.65306122 + 22.65306122 + -1.204081633x + x2 = 0 + 22.65306122 Combine like terms: -22.65306122 + 22.65306122 = 0.00000000 0.00000000 + -1.204081633x + x2 = 0 + 22.65306122 -1.204081633x + x2 = 0 + 22.65306122 Combine like terms: 0 + 22.65306122 = 22.65306122 -1.204081633x + x2 = 22.65306122 The x term is -1.204081633x. Take half its coefficient (-0.6020408165). Square it (0.3624531447) and add it to both sides. Add '0.3624531447' to each side of the equation. -1.204081633x + 0.3624531447 + x2 = 22.65306122 + 0.3624531447 Reorder the terms: 0.3624531447 + -1.204081633x + x2 = 22.65306122 + 0.3624531447 Combine like terms: 22.65306122 + 0.3624531447 = 23.0155143647 0.3624531447 + -1.204081633x + x2 = 23.0155143647 Factor a perfect square on the left side: (x + -0.6020408165)(x + -0.6020408165) = 23.0155143647 Calculate the square root of the right side: 4.797448735 Break this problem into two subproblems by setting (x + -0.6020408165) equal to 4.797448735 and -4.797448735.Subproblem 1
x + -0.6020408165 = 4.797448735 Simplifying x + -0.6020408165 = 4.797448735 Reorder the terms: -0.6020408165 + x = 4.797448735 Solving -0.6020408165 + x = 4.797448735 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.6020408165' to each side of the equation. -0.6020408165 + 0.6020408165 + x = 4.797448735 + 0.6020408165 Combine like terms: -0.6020408165 + 0.6020408165 = 0.0000000000 0.0000000000 + x = 4.797448735 + 0.6020408165 x = 4.797448735 + 0.6020408165 Combine like terms: 4.797448735 + 0.6020408165 = 5.3994895515 x = 5.3994895515 Simplifying x = 5.3994895515Subproblem 2
x + -0.6020408165 = -4.797448735 Simplifying x + -0.6020408165 = -4.797448735 Reorder the terms: -0.6020408165 + x = -4.797448735 Solving -0.6020408165 + x = -4.797448735 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.6020408165' to each side of the equation. -0.6020408165 + 0.6020408165 + x = -4.797448735 + 0.6020408165 Combine like terms: -0.6020408165 + 0.6020408165 = 0.0000000000 0.0000000000 + x = -4.797448735 + 0.6020408165 x = -4.797448735 + 0.6020408165 Combine like terms: -4.797448735 + 0.6020408165 = -4.1954079185 x = -4.1954079185 Simplifying x = -4.1954079185Solution
The solution to the problem is based on the solutions from the subproblems. x = {5.3994895515, -4.1954079185}
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