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Simplifying 0 = -4.9x2 + 10x + 50 Reorder the terms: 0 = 50 + 10x + -4.9x2 Solving 0 = 50 + 10x + -4.9x2 Solving for variable 'x'. Combine like terms: 0 + -50 = -50 -50 + -10x + 4.9x2 = 50 + 10x + -4.9x2 + -50 + -10x + 4.9x2 Reorder the terms: -50 + -10x + 4.9x2 = 50 + -50 + 10x + -10x + -4.9x2 + 4.9x2 Combine like terms: 50 + -50 = 0 -50 + -10x + 4.9x2 = 0 + 10x + -10x + -4.9x2 + 4.9x2 -50 + -10x + 4.9x2 = 10x + -10x + -4.9x2 + 4.9x2 Combine like terms: 10x + -10x = 0 -50 + -10x + 4.9x2 = 0 + -4.9x2 + 4.9x2 -50 + -10x + 4.9x2 = -4.9x2 + 4.9x2 Combine like terms: -4.9x2 + 4.9x2 = 0.0 -50 + -10x + 4.9x2 = 0.0 Begin completing the square. Divide all terms by 4.9 the coefficient of the squared term: Divide each side by '4.9'. -10.20408163 + -2.040816327x + x2 = 0 Move the constant term to the right: Add '10.20408163' to each side of the equation. -10.20408163 + -2.040816327x + 10.20408163 + x2 = 0 + 10.20408163 Reorder the terms: -10.20408163 + 10.20408163 + -2.040816327x + x2 = 0 + 10.20408163 Combine like terms: -10.20408163 + 10.20408163 = 0.00000000 0.00000000 + -2.040816327x + x2 = 0 + 10.20408163 -2.040816327x + x2 = 0 + 10.20408163 Combine like terms: 0 + 10.20408163 = 10.20408163 -2.040816327x + x2 = 10.20408163 The x term is -2.040816327x. Take half its coefficient (-1.020408164). Square it (1.041232821) and add it to both sides. Add '1.041232821' to each side of the equation. -2.040816327x + 1.041232821 + x2 = 10.20408163 + 1.041232821 Reorder the terms: 1.041232821 + -2.040816327x + x2 = 10.20408163 + 1.041232821 Combine like terms: 10.20408163 + 1.041232821 = 11.245314451 1.041232821 + -2.040816327x + x2 = 11.245314451 Factor a perfect square on the left side: (x + -1.020408164)(x + -1.020408164) = 11.245314451 Calculate the square root of the right side: 3.353403413 Break this problem into two subproblems by setting (x + -1.020408164) equal to 3.353403413 and -3.353403413.Subproblem 1
x + -1.020408164 = 3.353403413 Simplifying x + -1.020408164 = 3.353403413 Reorder the terms: -1.020408164 + x = 3.353403413 Solving -1.020408164 + x = 3.353403413 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.020408164' to each side of the equation. -1.020408164 + 1.020408164 + x = 3.353403413 + 1.020408164 Combine like terms: -1.020408164 + 1.020408164 = 0.000000000 0.000000000 + x = 3.353403413 + 1.020408164 x = 3.353403413 + 1.020408164 Combine like terms: 3.353403413 + 1.020408164 = 4.373811577 x = 4.373811577 Simplifying x = 4.373811577Subproblem 2
x + -1.020408164 = -3.353403413 Simplifying x + -1.020408164 = -3.353403413 Reorder the terms: -1.020408164 + x = -3.353403413 Solving -1.020408164 + x = -3.353403413 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.020408164' to each side of the equation. -1.020408164 + 1.020408164 + x = -3.353403413 + 1.020408164 Combine like terms: -1.020408164 + 1.020408164 = 0.000000000 0.000000000 + x = -3.353403413 + 1.020408164 x = -3.353403413 + 1.020408164 Combine like terms: -3.353403413 + 1.020408164 = -2.332995249 x = -2.332995249 Simplifying x = -2.332995249Solution
The solution to the problem is based on the solutions from the subproblems. x = {4.373811577, -2.332995249}
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