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Simplifying 0 = -16x2 + 220x + -390 Reorder the terms: 0 = -390 + 220x + -16x2 Solving 0 = -390 + 220x + -16x2 Solving for variable 'x'. Combine like terms: 0 + 390 = 390 390 + -220x + 16x2 = -390 + 220x + -16x2 + 390 + -220x + 16x2 Reorder the terms: 390 + -220x + 16x2 = -390 + 390 + 220x + -220x + -16x2 + 16x2 Combine like terms: -390 + 390 = 0 390 + -220x + 16x2 = 0 + 220x + -220x + -16x2 + 16x2 390 + -220x + 16x2 = 220x + -220x + -16x2 + 16x2 Combine like terms: 220x + -220x = 0 390 + -220x + 16x2 = 0 + -16x2 + 16x2 390 + -220x + 16x2 = -16x2 + 16x2 Combine like terms: -16x2 + 16x2 = 0 390 + -220x + 16x2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(195 + -110x + 8x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(195 + -110x + 8x2)' equal to zero and attempt to solve: Simplifying 195 + -110x + 8x2 = 0 Solving 195 + -110x + 8x2 = 0 Begin completing the square. Divide all terms by 8 the coefficient of the squared term: Divide each side by '8'. 24.375 + -13.75x + x2 = 0 Move the constant term to the right: Add '-24.375' to each side of the equation. 24.375 + -13.75x + -24.375 + x2 = 0 + -24.375 Reorder the terms: 24.375 + -24.375 + -13.75x + x2 = 0 + -24.375 Combine like terms: 24.375 + -24.375 = 0.000 0.000 + -13.75x + x2 = 0 + -24.375 -13.75x + x2 = 0 + -24.375 Combine like terms: 0 + -24.375 = -24.375 -13.75x + x2 = -24.375 The x term is -13.75x. Take half its coefficient (-6.875). Square it (47.265625) and add it to both sides. Add '47.265625' to each side of the equation. -13.75x + 47.265625 + x2 = -24.375 + 47.265625 Reorder the terms: 47.265625 + -13.75x + x2 = -24.375 + 47.265625 Combine like terms: -24.375 + 47.265625 = 22.890625 47.265625 + -13.75x + x2 = 22.890625 Factor a perfect square on the left side: (x + -6.875)(x + -6.875) = 22.890625 Calculate the square root of the right side: 4.784414802 Break this problem into two subproblems by setting (x + -6.875) equal to 4.784414802 and -4.784414802.Subproblem 1
x + -6.875 = 4.784414802 Simplifying x + -6.875 = 4.784414802 Reorder the terms: -6.875 + x = 4.784414802 Solving -6.875 + x = 4.784414802 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '6.875' to each side of the equation. -6.875 + 6.875 + x = 4.784414802 + 6.875 Combine like terms: -6.875 + 6.875 = 0.000 0.000 + x = 4.784414802 + 6.875 x = 4.784414802 + 6.875 Combine like terms: 4.784414802 + 6.875 = 11.659414802 x = 11.659414802 Simplifying x = 11.659414802Subproblem 2
x + -6.875 = -4.784414802 Simplifying x + -6.875 = -4.784414802 Reorder the terms: -6.875 + x = -4.784414802 Solving -6.875 + x = -4.784414802 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '6.875' to each side of the equation. -6.875 + 6.875 + x = -4.784414802 + 6.875 Combine like terms: -6.875 + 6.875 = 0.000 0.000 + x = -4.784414802 + 6.875 x = -4.784414802 + 6.875 Combine like terms: -4.784414802 + 6.875 = 2.090585198 x = 2.090585198 Simplifying x = 2.090585198Solution
The solution to the problem is based on the solutions from the subproblems. x = {11.659414802, 2.090585198}Solution
x = {11.659414802, 2.090585198}
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