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Simplifying 54x2 + 2x + -123 = 0 Reorder the terms: -123 + 2x + 54x2 = 0 Solving -123 + 2x + 54x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 54 the coefficient of the squared term: Divide each side by '54'. -2.277777778 + 0.03703703704x + x2 = 0 Move the constant term to the right: Add '2.277777778' to each side of the equation. -2.277777778 + 0.03703703704x + 2.277777778 + x2 = 0 + 2.277777778 Reorder the terms: -2.277777778 + 2.277777778 + 0.03703703704x + x2 = 0 + 2.277777778 Combine like terms: -2.277777778 + 2.277777778 = 0.000000000 0.000000000 + 0.03703703704x + x2 = 0 + 2.277777778 0.03703703704x + x2 = 0 + 2.277777778 Combine like terms: 0 + 2.277777778 = 2.277777778 0.03703703704x + x2 = 2.277777778 The x term is 0.03703703704x. Take half its coefficient (0.01851851852). Square it (0.0003429355282) and add it to both sides. Add '0.0003429355282' to each side of the equation. 0.03703703704x + 0.0003429355282 + x2 = 2.277777778 + 0.0003429355282 Reorder the terms: 0.0003429355282 + 0.03703703704x + x2 = 2.277777778 + 0.0003429355282 Combine like terms: 2.277777778 + 0.0003429355282 = 2.2781207135282 0.0003429355282 + 0.03703703704x + x2 = 2.2781207135282 Factor a perfect square on the left side: (x + 0.01851851852)(x + 0.01851851852) = 2.2781207135282 Calculate the square root of the right side: 1.509344465 Break this problem into two subproblems by setting (x + 0.01851851852) equal to 1.509344465 and -1.509344465.Subproblem 1
x + 0.01851851852 = 1.509344465 Simplifying x + 0.01851851852 = 1.509344465 Reorder the terms: 0.01851851852 + x = 1.509344465 Solving 0.01851851852 + x = 1.509344465 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.01851851852' to each side of the equation. 0.01851851852 + -0.01851851852 + x = 1.509344465 + -0.01851851852 Combine like terms: 0.01851851852 + -0.01851851852 = 0.00000000000 0.00000000000 + x = 1.509344465 + -0.01851851852 x = 1.509344465 + -0.01851851852 Combine like terms: 1.509344465 + -0.01851851852 = 1.49082594648 x = 1.49082594648 Simplifying x = 1.49082594648Subproblem 2
x + 0.01851851852 = -1.509344465 Simplifying x + 0.01851851852 = -1.509344465 Reorder the terms: 0.01851851852 + x = -1.509344465 Solving 0.01851851852 + x = -1.509344465 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.01851851852' to each side of the equation. 0.01851851852 + -0.01851851852 + x = -1.509344465 + -0.01851851852 Combine like terms: 0.01851851852 + -0.01851851852 = 0.00000000000 0.00000000000 + x = -1.509344465 + -0.01851851852 x = -1.509344465 + -0.01851851852 Combine like terms: -1.509344465 + -0.01851851852 = -1.52786298352 x = -1.52786298352 Simplifying x = -1.52786298352Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.49082594648, -1.52786298352}
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