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Simplifying 4.9x2 + 15x + -1.2 = 0 Reorder the terms: -1.2 + 15x + 4.9x2 = 0 Solving -1.2 + 15x + 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'. -0.2448979592 + 3.06122449x + x2 = 0 Move the constant term to the right: Add '0.2448979592' to each side of the equation. -0.2448979592 + 3.06122449x + 0.2448979592 + x2 = 0 + 0.2448979592 Reorder the terms: -0.2448979592 + 0.2448979592 + 3.06122449x + x2 = 0 + 0.2448979592 Combine like terms: -0.2448979592 + 0.2448979592 = 0.0000000000 0.0000000000 + 3.06122449x + x2 = 0 + 0.2448979592 3.06122449x + x2 = 0 + 0.2448979592 Combine like terms: 0 + 0.2448979592 = 0.2448979592 3.06122449x + x2 = 0.2448979592 The x term is 3.06122449x. Take half its coefficient (1.530612245). Square it (2.342773845) and add it to both sides. Add '2.342773845' to each side of the equation. 3.06122449x + 2.342773845 + x2 = 0.2448979592 + 2.342773845 Reorder the terms: 2.342773845 + 3.06122449x + x2 = 0.2448979592 + 2.342773845 Combine like terms: 0.2448979592 + 2.342773845 = 2.5876718042 2.342773845 + 3.06122449x + x2 = 2.5876718042 Factor a perfect square on the left side: (x + 1.530612245)(x + 1.530612245) = 2.5876718042 Calculate the square root of the right side: 1.608624196 Break this problem into two subproblems by setting (x + 1.530612245) equal to 1.608624196 and -1.608624196.Subproblem 1
x + 1.530612245 = 1.608624196 Simplifying x + 1.530612245 = 1.608624196 Reorder the terms: 1.530612245 + x = 1.608624196 Solving 1.530612245 + x = 1.608624196 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.530612245' to each side of the equation. 1.530612245 + -1.530612245 + x = 1.608624196 + -1.530612245 Combine like terms: 1.530612245 + -1.530612245 = 0.000000000 0.000000000 + x = 1.608624196 + -1.530612245 x = 1.608624196 + -1.530612245 Combine like terms: 1.608624196 + -1.530612245 = 0.078011951 x = 0.078011951 Simplifying x = 0.078011951Subproblem 2
x + 1.530612245 = -1.608624196 Simplifying x + 1.530612245 = -1.608624196 Reorder the terms: 1.530612245 + x = -1.608624196 Solving 1.530612245 + x = -1.608624196 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.530612245' to each side of the equation. 1.530612245 + -1.530612245 + x = -1.608624196 + -1.530612245 Combine like terms: 1.530612245 + -1.530612245 = 0.000000000 0.000000000 + x = -1.608624196 + -1.530612245 x = -1.608624196 + -1.530612245 Combine like terms: -1.608624196 + -1.530612245 = -3.139236441 x = -3.139236441 Simplifying x = -3.139236441Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.078011951, -3.139236441}
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