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Simplifying -23 = -4.9x2 + 15x Reorder the terms: -23 = 15x + -4.9x2 Solving -23 = 15x + -4.9x2 Solving for variable 'x'. Reorder the terms: -23 + -15x + 4.9x2 = 15x + -15x + -4.9x2 + 4.9x2 Combine like terms: 15x + -15x = 0 -23 + -15x + 4.9x2 = 0 + -4.9x2 + 4.9x2 -23 + -15x + 4.9x2 = -4.9x2 + 4.9x2 Combine like terms: -4.9x2 + 4.9x2 = 0.0 -23 + -15x + 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'. -4.693877551 + -3.06122449x + x2 = 0 Move the constant term to the right: Add '4.693877551' to each side of the equation. -4.693877551 + -3.06122449x + 4.693877551 + x2 = 0 + 4.693877551 Reorder the terms: -4.693877551 + 4.693877551 + -3.06122449x + x2 = 0 + 4.693877551 Combine like terms: -4.693877551 + 4.693877551 = 0.000000000 0.000000000 + -3.06122449x + x2 = 0 + 4.693877551 -3.06122449x + x2 = 0 + 4.693877551 Combine like terms: 0 + 4.693877551 = 4.693877551 -3.06122449x + x2 = 4.693877551 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 = 4.693877551 + 2.342773845 Reorder the terms: 2.342773845 + -3.06122449x + x2 = 4.693877551 + 2.342773845 Combine like terms: 4.693877551 + 2.342773845 = 7.036651396 2.342773845 + -3.06122449x + x2 = 7.036651396 Factor a perfect square on the left side: (x + -1.530612245)(x + -1.530612245) = 7.036651396 Calculate the square root of the right side: 2.652668731 Break this problem into two subproblems by setting (x + -1.530612245) equal to 2.652668731 and -2.652668731.Subproblem 1
x + -1.530612245 = 2.652668731 Simplifying x + -1.530612245 = 2.652668731 Reorder the terms: -1.530612245 + x = 2.652668731 Solving -1.530612245 + x = 2.652668731 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 = 2.652668731 + 1.530612245 Combine like terms: -1.530612245 + 1.530612245 = 0.000000000 0.000000000 + x = 2.652668731 + 1.530612245 x = 2.652668731 + 1.530612245 Combine like terms: 2.652668731 + 1.530612245 = 4.183280976 x = 4.183280976 Simplifying x = 4.183280976Subproblem 2
x + -1.530612245 = -2.652668731 Simplifying x + -1.530612245 = -2.652668731 Reorder the terms: -1.530612245 + x = -2.652668731 Solving -1.530612245 + x = -2.652668731 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 = -2.652668731 + 1.530612245 Combine like terms: -1.530612245 + 1.530612245 = 0.000000000 0.000000000 + x = -2.652668731 + 1.530612245 x = -2.652668731 + 1.530612245 Combine like terms: -2.652668731 + 1.530612245 = -1.122056486 x = -1.122056486 Simplifying x = -1.122056486Solution
The solution to the problem is based on the solutions from the subproblems. x = {4.183280976, -1.122056486}
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