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Simplifying -165x2 + 15.68x + 16.464 = 0 Reorder the terms: 16.464 + 15.68x + -165x2 = 0 Solving 16.464 + 15.68x + -165x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by -165 the coefficient of the squared term: Divide each side by '-165'. -0.09978181818 + -0.09503030303x + x2 = 0 Move the constant term to the right: Add '0.09978181818' to each side of the equation. -0.09978181818 + -0.09503030303x + 0.09978181818 + x2 = 0 + 0.09978181818 Reorder the terms: -0.09978181818 + 0.09978181818 + -0.09503030303x + x2 = 0 + 0.09978181818 Combine like terms: -0.09978181818 + 0.09978181818 = 0.00000000000 0.00000000000 + -0.09503030303x + x2 = 0 + 0.09978181818 -0.09503030303x + x2 = 0 + 0.09978181818 Combine like terms: 0 + 0.09978181818 = 0.09978181818 -0.09503030303x + x2 = 0.09978181818 The x term is -0.09503030303x. Take half its coefficient (-0.04751515152). Square it (0.002257689624) and add it to both sides. Add '0.002257689624' to each side of the equation. -0.09503030303x + 0.002257689624 + x2 = 0.09978181818 + 0.002257689624 Reorder the terms: 0.002257689624 + -0.09503030303x + x2 = 0.09978181818 + 0.002257689624 Combine like terms: 0.09978181818 + 0.002257689624 = 0.102039507804 0.002257689624 + -0.09503030303x + x2 = 0.102039507804 Factor a perfect square on the left side: (x + -0.04751515152)(x + -0.04751515152) = 0.102039507804 Calculate the square root of the right side: 0.319436234 Break this problem into two subproblems by setting (x + -0.04751515152) equal to 0.319436234 and -0.319436234.Subproblem 1
x + -0.04751515152 = 0.319436234 Simplifying x + -0.04751515152 = 0.319436234 Reorder the terms: -0.04751515152 + x = 0.319436234 Solving -0.04751515152 + x = 0.319436234 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.04751515152' to each side of the equation. -0.04751515152 + 0.04751515152 + x = 0.319436234 + 0.04751515152 Combine like terms: -0.04751515152 + 0.04751515152 = 0.00000000000 0.00000000000 + x = 0.319436234 + 0.04751515152 x = 0.319436234 + 0.04751515152 Combine like terms: 0.319436234 + 0.04751515152 = 0.36695138552 x = 0.36695138552 Simplifying x = 0.36695138552Subproblem 2
x + -0.04751515152 = -0.319436234 Simplifying x + -0.04751515152 = -0.319436234 Reorder the terms: -0.04751515152 + x = -0.319436234 Solving -0.04751515152 + x = -0.319436234 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.04751515152' to each side of the equation. -0.04751515152 + 0.04751515152 + x = -0.319436234 + 0.04751515152 Combine like terms: -0.04751515152 + 0.04751515152 = 0.00000000000 0.00000000000 + x = -0.319436234 + 0.04751515152 x = -0.319436234 + 0.04751515152 Combine like terms: -0.319436234 + 0.04751515152 = -0.27192108248 x = -0.27192108248 Simplifying x = -0.27192108248Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.36695138552, -0.27192108248}
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