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Simplifying 0 = -18.4x2 + 24x + 3 Reorder the terms: 0 = 3 + 24x + -18.4x2 Solving 0 = 3 + 24x + -18.4x2 Solving for variable 'x'. Combine like terms: 0 + -3 = -3 -3 + -24x + 18.4x2 = 3 + 24x + -18.4x2 + -3 + -24x + 18.4x2 Reorder the terms: -3 + -24x + 18.4x2 = 3 + -3 + 24x + -24x + -18.4x2 + 18.4x2 Combine like terms: 3 + -3 = 0 -3 + -24x + 18.4x2 = 0 + 24x + -24x + -18.4x2 + 18.4x2 -3 + -24x + 18.4x2 = 24x + -24x + -18.4x2 + 18.4x2 Combine like terms: 24x + -24x = 0 -3 + -24x + 18.4x2 = 0 + -18.4x2 + 18.4x2 -3 + -24x + 18.4x2 = -18.4x2 + 18.4x2 Combine like terms: -18.4x2 + 18.4x2 = 0.0 -3 + -24x + 18.4x2 = 0.0 Begin completing the square. Divide all terms by 18.4 the coefficient of the squared term: Divide each side by '18.4'. -0.1630434783 + -1.304347826x + x2 = 0 Move the constant term to the right: Add '0.1630434783' to each side of the equation. -0.1630434783 + -1.304347826x + 0.1630434783 + x2 = 0 + 0.1630434783 Reorder the terms: -0.1630434783 + 0.1630434783 + -1.304347826x + x2 = 0 + 0.1630434783 Combine like terms: -0.1630434783 + 0.1630434783 = 0.0000000000 0.0000000000 + -1.304347826x + x2 = 0 + 0.1630434783 -1.304347826x + x2 = 0 + 0.1630434783 Combine like terms: 0 + 0.1630434783 = 0.1630434783 -1.304347826x + x2 = 0.1630434783 The x term is -1.304347826x. Take half its coefficient (-0.652173913). Square it (0.4253308128) and add it to both sides. Add '0.4253308128' to each side of the equation. -1.304347826x + 0.4253308128 + x2 = 0.1630434783 + 0.4253308128 Reorder the terms: 0.4253308128 + -1.304347826x + x2 = 0.1630434783 + 0.4253308128 Combine like terms: 0.1630434783 + 0.4253308128 = 0.5883742911 0.4253308128 + -1.304347826x + x2 = 0.5883742911 Factor a perfect square on the left side: (x + -0.652173913)(x + -0.652173913) = 0.5883742911 Calculate the square root of the right side: 0.767055598 Break this problem into two subproblems by setting (x + -0.652173913) equal to 0.767055598 and -0.767055598.Subproblem 1
x + -0.652173913 = 0.767055598 Simplifying x + -0.652173913 = 0.767055598 Reorder the terms: -0.652173913 + x = 0.767055598 Solving -0.652173913 + x = 0.767055598 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.652173913' to each side of the equation. -0.652173913 + 0.652173913 + x = 0.767055598 + 0.652173913 Combine like terms: -0.652173913 + 0.652173913 = 0.000000000 0.000000000 + x = 0.767055598 + 0.652173913 x = 0.767055598 + 0.652173913 Combine like terms: 0.767055598 + 0.652173913 = 1.419229511 x = 1.419229511 Simplifying x = 1.419229511Subproblem 2
x + -0.652173913 = -0.767055598 Simplifying x + -0.652173913 = -0.767055598 Reorder the terms: -0.652173913 + x = -0.767055598 Solving -0.652173913 + x = -0.767055598 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.652173913' to each side of the equation. -0.652173913 + 0.652173913 + x = -0.767055598 + 0.652173913 Combine like terms: -0.652173913 + 0.652173913 = 0.000000000 0.000000000 + x = -0.767055598 + 0.652173913 x = -0.767055598 + 0.652173913 Combine like terms: -0.767055598 + 0.652173913 = -0.114881685 x = -0.114881685 Simplifying x = -0.114881685Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.419229511, -0.114881685}
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