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Simplifying 3 = 4.905(x2) + x Reorder the terms: 3 = x + 4.905x2 Solving 3 = x + 4.905x2 Solving for variable 'x'. Reorder the terms: 3 + -1x + -4.905x2 = x + -1x + 4.905x2 + -4.905x2 Combine like terms: x + -1x = 0 3 + -1x + -4.905x2 = 0 + 4.905x2 + -4.905x2 3 + -1x + -4.905x2 = 4.905x2 + -4.905x2 Combine like terms: 4.905x2 + -4.905x2 = 0.000 3 + -1x + -4.905x2 = 0.000 Begin completing the square. Divide all terms by -4.905 the coefficient of the squared term: Divide each side by '-4.905'. -0.6116207951 + 0.2038735984x + x2 = 0 Move the constant term to the right: Add '0.6116207951' to each side of the equation. -0.6116207951 + 0.2038735984x + 0.6116207951 + x2 = 0 + 0.6116207951 Reorder the terms: -0.6116207951 + 0.6116207951 + 0.2038735984x + x2 = 0 + 0.6116207951 Combine like terms: -0.6116207951 + 0.6116207951 = 0.0000000000 0.0000000000 + 0.2038735984x + x2 = 0 + 0.6116207951 0.2038735984x + x2 = 0 + 0.6116207951 Combine like terms: 0 + 0.6116207951 = 0.6116207951 0.2038735984x + x2 = 0.6116207951 The x term is 0.2038735984x. Take half its coefficient (0.1019367992). Square it (0.01039111103) and add it to both sides. Add '0.01039111103' to each side of the equation. 0.2038735984x + 0.01039111103 + x2 = 0.6116207951 + 0.01039111103 Reorder the terms: 0.01039111103 + 0.2038735984x + x2 = 0.6116207951 + 0.01039111103 Combine like terms: 0.6116207951 + 0.01039111103 = 0.62201190613 0.01039111103 + 0.2038735984x + x2 = 0.62201190613 Factor a perfect square on the left side: (x + 0.1019367992)(x + 0.1019367992) = 0.62201190613 Calculate the square root of the right side: 0.788677314 Break this problem into two subproblems by setting (x + 0.1019367992) equal to 0.788677314 and -0.788677314.Subproblem 1
x + 0.1019367992 = 0.788677314 Simplifying x + 0.1019367992 = 0.788677314 Reorder the terms: 0.1019367992 + x = 0.788677314 Solving 0.1019367992 + x = 0.788677314 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.1019367992' to each side of the equation. 0.1019367992 + -0.1019367992 + x = 0.788677314 + -0.1019367992 Combine like terms: 0.1019367992 + -0.1019367992 = 0.0000000000 0.0000000000 + x = 0.788677314 + -0.1019367992 x = 0.788677314 + -0.1019367992 Combine like terms: 0.788677314 + -0.1019367992 = 0.6867405148 x = 0.6867405148 Simplifying x = 0.6867405148Subproblem 2
x + 0.1019367992 = -0.788677314 Simplifying x + 0.1019367992 = -0.788677314 Reorder the terms: 0.1019367992 + x = -0.788677314 Solving 0.1019367992 + x = -0.788677314 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.1019367992' to each side of the equation. 0.1019367992 + -0.1019367992 + x = -0.788677314 + -0.1019367992 Combine like terms: 0.1019367992 + -0.1019367992 = 0.0000000000 0.0000000000 + x = -0.788677314 + -0.1019367992 x = -0.788677314 + -0.1019367992 Combine like terms: -0.788677314 + -0.1019367992 = -0.8906141132 x = -0.8906141132 Simplifying x = -0.8906141132Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.6867405148, -0.8906141132}
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