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Simplifying 0 = 1.5 + 10x + 0.5 * -9.8x2 Multiply 0.5 * -9.8 0 = 1.5 + 10x + -4.9x2 Solving 0 = 1.5 + 10x + -4.9x2 Solving for variable 'x'. Combine like terms: 0 + -1.5 = -1.5 -1.5 + -10x + 4.9x2 = 1.5 + 10x + -4.9x2 + -1.5 + -10x + 4.9x2 Reorder the terms: -1.5 + -10x + 4.9x2 = 1.5 + -1.5 + 10x + -10x + -4.9x2 + 4.9x2 Combine like terms: 1.5 + -1.5 = 0.0 -1.5 + -10x + 4.9x2 = 0.0 + 10x + -10x + -4.9x2 + 4.9x2 -1.5 + -10x + 4.9x2 = 10x + -10x + -4.9x2 + 4.9x2 Combine like terms: 10x + -10x = 0 -1.5 + -10x + 4.9x2 = 0 + -4.9x2 + 4.9x2 -1.5 + -10x + 4.9x2 = -4.9x2 + 4.9x2 Combine like terms: -4.9x2 + 4.9x2 = 0.0 -1.5 + -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'. -0.306122449 + -2.040816327x + x2 = 0 Move the constant term to the right: Add '0.306122449' to each side of the equation. -0.306122449 + -2.040816327x + 0.306122449 + x2 = 0 + 0.306122449 Reorder the terms: -0.306122449 + 0.306122449 + -2.040816327x + x2 = 0 + 0.306122449 Combine like terms: -0.306122449 + 0.306122449 = 0.000000000 0.000000000 + -2.040816327x + x2 = 0 + 0.306122449 -2.040816327x + x2 = 0 + 0.306122449 Combine like terms: 0 + 0.306122449 = 0.306122449 -2.040816327x + x2 = 0.306122449 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 = 0.306122449 + 1.041232821 Reorder the terms: 1.041232821 + -2.040816327x + x2 = 0.306122449 + 1.041232821 Combine like terms: 0.306122449 + 1.041232821 = 1.34735527 1.041232821 + -2.040816327x + x2 = 1.34735527 Factor a perfect square on the left side: (x + -1.020408164)(x + -1.020408164) = 1.34735527 Calculate the square root of the right side: 1.160756335 Break this problem into two subproblems by setting (x + -1.020408164) equal to 1.160756335 and -1.160756335.Subproblem 1
x + -1.020408164 = 1.160756335 Simplifying x + -1.020408164 = 1.160756335 Reorder the terms: -1.020408164 + x = 1.160756335 Solving -1.020408164 + x = 1.160756335 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 = 1.160756335 + 1.020408164 Combine like terms: -1.020408164 + 1.020408164 = 0.000000000 0.000000000 + x = 1.160756335 + 1.020408164 x = 1.160756335 + 1.020408164 Combine like terms: 1.160756335 + 1.020408164 = 2.181164499 x = 2.181164499 Simplifying x = 2.181164499Subproblem 2
x + -1.020408164 = -1.160756335 Simplifying x + -1.020408164 = -1.160756335 Reorder the terms: -1.020408164 + x = -1.160756335 Solving -1.020408164 + x = -1.160756335 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 = -1.160756335 + 1.020408164 Combine like terms: -1.020408164 + 1.020408164 = 0.000000000 0.000000000 + x = -1.160756335 + 1.020408164 x = -1.160756335 + 1.020408164 Combine like terms: -1.160756335 + 1.020408164 = -0.140348171 x = -0.140348171 Simplifying x = -0.140348171Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.181164499, -0.140348171}
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