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Simplifying 0 = 15x2 + -4 + 3x + -5x2 + -8 Reorder the terms: 0 = -4 + -8 + 3x + 15x2 + -5x2 Combine like terms: -4 + -8 = -12 0 = -12 + 3x + 15x2 + -5x2 Combine like terms: 15x2 + -5x2 = 10x2 0 = -12 + 3x + 10x2 Solving 0 = -12 + 3x + 10x2 Solving for variable 'x'. Combine like terms: 0 + 12 = 12 12 + -3x + -10x2 = -12 + 3x + 10x2 + 12 + -3x + -10x2 Reorder the terms: 12 + -3x + -10x2 = -12 + 12 + 3x + -3x + 10x2 + -10x2 Combine like terms: -12 + 12 = 0 12 + -3x + -10x2 = 0 + 3x + -3x + 10x2 + -10x2 12 + -3x + -10x2 = 3x + -3x + 10x2 + -10x2 Combine like terms: 3x + -3x = 0 12 + -3x + -10x2 = 0 + 10x2 + -10x2 12 + -3x + -10x2 = 10x2 + -10x2 Combine like terms: 10x2 + -10x2 = 0 12 + -3x + -10x2 = 0 Begin completing the square. Divide all terms by -10 the coefficient of the squared term: Divide each side by '-10'. -1.2 + 0.3x + x2 = 0 Move the constant term to the right: Add '1.2' to each side of the equation. -1.2 + 0.3x + 1.2 + x2 = 0 + 1.2 Reorder the terms: -1.2 + 1.2 + 0.3x + x2 = 0 + 1.2 Combine like terms: -1.2 + 1.2 = 0.0 0.0 + 0.3x + x2 = 0 + 1.2 0.3x + x2 = 0 + 1.2 Combine like terms: 0 + 1.2 = 1.2 0.3x + x2 = 1.2 The x term is 0.3x. Take half its coefficient (0.15). Square it (0.0225) and add it to both sides. Add '0.0225' to each side of the equation. 0.3x + 0.0225 + x2 = 1.2 + 0.0225 Reorder the terms: 0.0225 + 0.3x + x2 = 1.2 + 0.0225 Combine like terms: 1.2 + 0.0225 = 1.2225 0.0225 + 0.3x + x2 = 1.2225 Factor a perfect square on the left side: (x + 0.15)(x + 0.15) = 1.2225 Calculate the square root of the right side: 1.105667219 Break this problem into two subproblems by setting (x + 0.15) equal to 1.105667219 and -1.105667219.Subproblem 1
x + 0.15 = 1.105667219 Simplifying x + 0.15 = 1.105667219 Reorder the terms: 0.15 + x = 1.105667219 Solving 0.15 + x = 1.105667219 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.15' to each side of the equation. 0.15 + -0.15 + x = 1.105667219 + -0.15 Combine like terms: 0.15 + -0.15 = 0.00 0.00 + x = 1.105667219 + -0.15 x = 1.105667219 + -0.15 Combine like terms: 1.105667219 + -0.15 = 0.955667219 x = 0.955667219 Simplifying x = 0.955667219Subproblem 2
x + 0.15 = -1.105667219 Simplifying x + 0.15 = -1.105667219 Reorder the terms: 0.15 + x = -1.105667219 Solving 0.15 + x = -1.105667219 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.15' to each side of the equation. 0.15 + -0.15 + x = -1.105667219 + -0.15 Combine like terms: 0.15 + -0.15 = 0.00 0.00 + x = -1.105667219 + -0.15 x = -1.105667219 + -0.15 Combine like terms: -1.105667219 + -0.15 = -1.255667219 x = -1.255667219 Simplifying x = -1.255667219Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.955667219, -1.255667219}
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