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Simplifying 4.9x2 + -30x + 23 = 0 Reorder the terms: 23 + -30x + 4.9x2 = 0 Solving 23 + -30x + 4.9x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 4.9 the coefficient of the squared term: Divide each side by '4.9'. 4.693877551 + -6.12244898x + x2 = 0 Move the constant term to the right: Add '-4.693877551' to each side of the equation. 4.693877551 + -6.12244898x + -4.693877551 + x2 = 0 + -4.693877551 Reorder the terms: 4.693877551 + -4.693877551 + -6.12244898x + x2 = 0 + -4.693877551 Combine like terms: 4.693877551 + -4.693877551 = 0.000000000 0.000000000 + -6.12244898x + x2 = 0 + -4.693877551 -6.12244898x + x2 = 0 + -4.693877551 Combine like terms: 0 + -4.693877551 = -4.693877551 -6.12244898x + x2 = -4.693877551 The x term is -6.12244898x. Take half its coefficient (-3.06122449). Square it (9.371095378) and add it to both sides. Add '9.371095378' to each side of the equation. -6.12244898x + 9.371095378 + x2 = -4.693877551 + 9.371095378 Reorder the terms: 9.371095378 + -6.12244898x + x2 = -4.693877551 + 9.371095378 Combine like terms: -4.693877551 + 9.371095378 = 4.677217827 9.371095378 + -6.12244898x + x2 = 4.677217827 Factor a perfect square on the left side: (x + -3.06122449)(x + -3.06122449) = 4.677217827 Calculate the square root of the right side: 2.16268764 Break this problem into two subproblems by setting (x + -3.06122449) equal to 2.16268764 and -2.16268764.Subproblem 1
x + -3.06122449 = 2.16268764 Simplifying x + -3.06122449 = 2.16268764 Reorder the terms: -3.06122449 + x = 2.16268764 Solving -3.06122449 + x = 2.16268764 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '3.06122449' to each side of the equation. -3.06122449 + 3.06122449 + x = 2.16268764 + 3.06122449 Combine like terms: -3.06122449 + 3.06122449 = 0.00000000 0.00000000 + x = 2.16268764 + 3.06122449 x = 2.16268764 + 3.06122449 Combine like terms: 2.16268764 + 3.06122449 = 5.22391213 x = 5.22391213 Simplifying x = 5.22391213Subproblem 2
x + -3.06122449 = -2.16268764 Simplifying x + -3.06122449 = -2.16268764 Reorder the terms: -3.06122449 + x = -2.16268764 Solving -3.06122449 + x = -2.16268764 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '3.06122449' to each side of the equation. -3.06122449 + 3.06122449 + x = -2.16268764 + 3.06122449 Combine like terms: -3.06122449 + 3.06122449 = 0.00000000 0.00000000 + x = -2.16268764 + 3.06122449 x = -2.16268764 + 3.06122449 Combine like terms: -2.16268764 + 3.06122449 = 0.89853685 x = 0.89853685 Simplifying x = 0.89853685Solution
The solution to the problem is based on the solutions from the subproblems. x = {5.22391213, 0.89853685}
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