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Simplifying (7x3 + 3x2 + 4x + 10) + -1(10 + 8x + 3x3) = 0 Reorder the terms: (10 + 4x + 3x2 + 7x3) + -1(10 + 8x + 3x3) = 0 Remove parenthesis around (10 + 4x + 3x2 + 7x3) 10 + 4x + 3x2 + 7x3 + -1(10 + 8x + 3x3) = 0 10 + 4x + 3x2 + 7x3 + (10 * -1 + 8x * -1 + 3x3 * -1) = 0 10 + 4x + 3x2 + 7x3 + (-10 + -8x + -3x3) = 0 Reorder the terms: 10 + -10 + 4x + -8x + 3x2 + 7x3 + -3x3 = 0 Combine like terms: 10 + -10 = 0 0 + 4x + -8x + 3x2 + 7x3 + -3x3 = 0 4x + -8x + 3x2 + 7x3 + -3x3 = 0 Combine like terms: 4x + -8x = -4x -4x + 3x2 + 7x3 + -3x3 = 0 Combine like terms: 7x3 + -3x3 = 4x3 -4x + 3x2 + 4x3 = 0 Solving -4x + 3x2 + 4x3 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), 'x'. x(-4 + 3x + 4x2) = 0Subproblem 1
Set the factor 'x' equal to zero and attempt to solve: Simplifying x = 0 Solving x = 0 Move all terms containing x to the left, all other terms to the right. Simplifying x = 0Subproblem 2
Set the factor '(-4 + 3x + 4x2)' equal to zero and attempt to solve: Simplifying -4 + 3x + 4x2 = 0 Solving -4 + 3x + 4x2 = 0 Begin completing the square. Divide all terms by 4 the coefficient of the squared term: Divide each side by '4'. -1 + 0.75x + x2 = 0 Move the constant term to the right: Add '1' to each side of the equation. -1 + 0.75x + 1 + x2 = 0 + 1 Reorder the terms: -1 + 1 + 0.75x + x2 = 0 + 1 Combine like terms: -1 + 1 = 0 0 + 0.75x + x2 = 0 + 1 0.75x + x2 = 0 + 1 Combine like terms: 0 + 1 = 1 0.75x + x2 = 1 The x term is 0.75x. Take half its coefficient (0.375). Square it (0.140625) and add it to both sides. Add '0.140625' to each side of the equation. 0.75x + 0.140625 + x2 = 1 + 0.140625 Reorder the terms: 0.140625 + 0.75x + x2 = 1 + 0.140625 Combine like terms: 1 + 0.140625 = 1.140625 0.140625 + 0.75x + x2 = 1.140625 Factor a perfect square on the left side: (x + 0.375)(x + 0.375) = 1.140625 Calculate the square root of the right side: 1.068000468 Break this problem into two subproblems by setting (x + 0.375) equal to 1.068000468 and -1.068000468.Subproblem 1
x + 0.375 = 1.068000468 Simplifying x + 0.375 = 1.068000468 Reorder the terms: 0.375 + x = 1.068000468 Solving 0.375 + x = 1.068000468 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.375' to each side of the equation. 0.375 + -0.375 + x = 1.068000468 + -0.375 Combine like terms: 0.375 + -0.375 = 0.000 0.000 + x = 1.068000468 + -0.375 x = 1.068000468 + -0.375 Combine like terms: 1.068000468 + -0.375 = 0.693000468 x = 0.693000468 Simplifying x = 0.693000468Subproblem 2
x + 0.375 = -1.068000468 Simplifying x + 0.375 = -1.068000468 Reorder the terms: 0.375 + x = -1.068000468 Solving 0.375 + x = -1.068000468 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.375' to each side of the equation. 0.375 + -0.375 + x = -1.068000468 + -0.375 Combine like terms: 0.375 + -0.375 = 0.000 0.000 + x = -1.068000468 + -0.375 x = -1.068000468 + -0.375 Combine like terms: -1.068000468 + -0.375 = -1.443000468 x = -1.443000468 Simplifying x = -1.443000468Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.693000468, -1.443000468}Solution
x = {0, 0.693000468, -1.443000468}
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