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Simplifying 315x2 + -448x + -156 = 0 Reorder the terms: -156 + -448x + 315x2 = 0 Solving -156 + -448x + 315x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 315 the coefficient of the squared term: Divide each side by '315'. -0.4952380952 + -1.422222222x + x2 = 0 Move the constant term to the right: Add '0.4952380952' to each side of the equation. -0.4952380952 + -1.422222222x + 0.4952380952 + x2 = 0 + 0.4952380952 Reorder the terms: -0.4952380952 + 0.4952380952 + -1.422222222x + x2 = 0 + 0.4952380952 Combine like terms: -0.4952380952 + 0.4952380952 = 0.0000000000 0.0000000000 + -1.422222222x + x2 = 0 + 0.4952380952 -1.422222222x + x2 = 0 + 0.4952380952 Combine like terms: 0 + 0.4952380952 = 0.4952380952 -1.422222222x + x2 = 0.4952380952 The x term is -1.422222222x. Take half its coefficient (-0.711111111). Square it (0.5056790122) and add it to both sides. Add '0.5056790122' to each side of the equation. -1.422222222x + 0.5056790122 + x2 = 0.4952380952 + 0.5056790122 Reorder the terms: 0.5056790122 + -1.422222222x + x2 = 0.4952380952 + 0.5056790122 Combine like terms: 0.4952380952 + 0.5056790122 = 1.0009171074 0.5056790122 + -1.422222222x + x2 = 1.0009171074 Factor a perfect square on the left side: (x + -0.711111111)(x + -0.711111111) = 1.0009171074 Calculate the square root of the right side: 1.000458449 Break this problem into two subproblems by setting (x + -0.711111111) equal to 1.000458449 and -1.000458449.Subproblem 1
x + -0.711111111 = 1.000458449 Simplifying x + -0.711111111 = 1.000458449 Reorder the terms: -0.711111111 + x = 1.000458449 Solving -0.711111111 + x = 1.000458449 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.711111111' to each side of the equation. -0.711111111 + 0.711111111 + x = 1.000458449 + 0.711111111 Combine like terms: -0.711111111 + 0.711111111 = 0.000000000 0.000000000 + x = 1.000458449 + 0.711111111 x = 1.000458449 + 0.711111111 Combine like terms: 1.000458449 + 0.711111111 = 1.71156956 x = 1.71156956 Simplifying x = 1.71156956Subproblem 2
x + -0.711111111 = -1.000458449 Simplifying x + -0.711111111 = -1.000458449 Reorder the terms: -0.711111111 + x = -1.000458449 Solving -0.711111111 + x = -1.000458449 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.711111111' to each side of the equation. -0.711111111 + 0.711111111 + x = -1.000458449 + 0.711111111 Combine like terms: -0.711111111 + 0.711111111 = 0.000000000 0.000000000 + x = -1.000458449 + 0.711111111 x = -1.000458449 + 0.711111111 Combine like terms: -1.000458449 + 0.711111111 = -0.289347338 x = -0.289347338 Simplifying x = -0.289347338Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.71156956, -0.289347338}
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