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Simplifying -4.9x2 + 10x + 15 = 0 Reorder the terms: 15 + 10x + -4.9x2 = 0 Solving 15 + 10x + -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'. -3.06122449 + -2.040816327x + x2 = 0 Move the constant term to the right: Add '3.06122449' to each side of the equation. -3.06122449 + -2.040816327x + 3.06122449 + x2 = 0 + 3.06122449 Reorder the terms: -3.06122449 + 3.06122449 + -2.040816327x + x2 = 0 + 3.06122449 Combine like terms: -3.06122449 + 3.06122449 = 0.00000000 0.00000000 + -2.040816327x + x2 = 0 + 3.06122449 -2.040816327x + x2 = 0 + 3.06122449 Combine like terms: 0 + 3.06122449 = 3.06122449 -2.040816327x + x2 = 3.06122449 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 = 3.06122449 + 1.041232821 Reorder the terms: 1.041232821 + -2.040816327x + x2 = 3.06122449 + 1.041232821 Combine like terms: 3.06122449 + 1.041232821 = 4.102457311 1.041232821 + -2.040816327x + x2 = 4.102457311 Factor a perfect square on the left side: (x + -1.020408164)(x + -1.020408164) = 4.102457311 Calculate the square root of the right side: 2.025452372 Break this problem into two subproblems by setting (x + -1.020408164) equal to 2.025452372 and -2.025452372.Subproblem 1
x + -1.020408164 = 2.025452372 Simplifying x + -1.020408164 = 2.025452372 Reorder the terms: -1.020408164 + x = 2.025452372 Solving -1.020408164 + x = 2.025452372 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 = 2.025452372 + 1.020408164 Combine like terms: -1.020408164 + 1.020408164 = 0.000000000 0.000000000 + x = 2.025452372 + 1.020408164 x = 2.025452372 + 1.020408164 Combine like terms: 2.025452372 + 1.020408164 = 3.045860536 x = 3.045860536 Simplifying x = 3.045860536Subproblem 2
x + -1.020408164 = -2.025452372 Simplifying x + -1.020408164 = -2.025452372 Reorder the terms: -1.020408164 + x = -2.025452372 Solving -1.020408164 + x = -2.025452372 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 = -2.025452372 + 1.020408164 Combine like terms: -1.020408164 + 1.020408164 = 0.000000000 0.000000000 + x = -2.025452372 + 1.020408164 x = -2.025452372 + 1.020408164 Combine like terms: -2.025452372 + 1.020408164 = -1.005044208 x = -1.005044208 Simplifying x = -1.005044208Solution
The solution to the problem is based on the solutions from the subproblems. x = {3.045860536, -1.005044208}
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