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Simplifying 148 + 5.2x + -4.9x2 = 0 Solving 148 + 5.2x + -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'. -30.20408163 + -1.06122449x + x2 = 0 Move the constant term to the right: Add '30.20408163' to each side of the equation. -30.20408163 + -1.06122449x + 30.20408163 + x2 = 0 + 30.20408163 Reorder the terms: -30.20408163 + 30.20408163 + -1.06122449x + x2 = 0 + 30.20408163 Combine like terms: -30.20408163 + 30.20408163 = 0.00000000 0.00000000 + -1.06122449x + x2 = 0 + 30.20408163 -1.06122449x + x2 = 0 + 30.20408163 Combine like terms: 0 + 30.20408163 = 30.20408163 -1.06122449x + x2 = 30.20408163 The x term is -1.06122449x. Take half its coefficient (-0.530612245). Square it (0.2815493545) and add it to both sides. Add '0.2815493545' to each side of the equation. -1.06122449x + 0.2815493545 + x2 = 30.20408163 + 0.2815493545 Reorder the terms: 0.2815493545 + -1.06122449x + x2 = 30.20408163 + 0.2815493545 Combine like terms: 30.20408163 + 0.2815493545 = 30.4856309845 0.2815493545 + -1.06122449x + x2 = 30.4856309845 Factor a perfect square on the left side: (x + -0.530612245)(x + -0.530612245) = 30.4856309845 Calculate the square root of the right side: 5.521379446 Break this problem into two subproblems by setting (x + -0.530612245) equal to 5.521379446 and -5.521379446.Subproblem 1
x + -0.530612245 = 5.521379446 Simplifying x + -0.530612245 = 5.521379446 Reorder the terms: -0.530612245 + x = 5.521379446 Solving -0.530612245 + x = 5.521379446 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.530612245' to each side of the equation. -0.530612245 + 0.530612245 + x = 5.521379446 + 0.530612245 Combine like terms: -0.530612245 + 0.530612245 = 0.000000000 0.000000000 + x = 5.521379446 + 0.530612245 x = 5.521379446 + 0.530612245 Combine like terms: 5.521379446 + 0.530612245 = 6.051991691 x = 6.051991691 Simplifying x = 6.051991691Subproblem 2
x + -0.530612245 = -5.521379446 Simplifying x + -0.530612245 = -5.521379446 Reorder the terms: -0.530612245 + x = -5.521379446 Solving -0.530612245 + x = -5.521379446 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.530612245' to each side of the equation. -0.530612245 + 0.530612245 + x = -5.521379446 + 0.530612245 Combine like terms: -0.530612245 + 0.530612245 = 0.000000000 0.000000000 + x = -5.521379446 + 0.530612245 x = -5.521379446 + 0.530612245 Combine like terms: -5.521379446 + 0.530612245 = -4.990767201 x = -4.990767201 Simplifying x = -4.990767201Solution
The solution to the problem is based on the solutions from the subproblems. x = {6.051991691, -4.990767201}
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